Event Study basic concept

BAB II

Konsep Dasar Event Study

Draft 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. 085823225666

1.    Konsep Synchronous or non-Synchronous Trading

·         Solibakke (2002), non-synchronous  trading suggest that individual asset prices are taken to be recorded at time intervals of one length when in fact, they are recorded at time intervals of others, possibly irregular, lengths.

·         Solibakke (2002),  event periods may change trading frequency due to higher information flow to the market and consequently generally higher financial press coverage. The change in trading frequency may change non-synchronous trading effect.

2.    Konsep  Volatility Clustering

·         Kothari and Warner (2004), We also touch upon the properties of the event study tests and examine the determinants of the properties as a function of firm characteristics, sample size, and event clustering, etc

·         Gershgoren (2006), Calendar Clustering, Here we present results for calendar clustering.The reason is that contemporaneous returns are likely to be more highly correlated across stocks than non-contemporaneous returns. With a correct model for mean returns, plus the fact that in such a model, the errors are (e.g. a factor model but not the CAPM, which must have cross-sectionally correlated errors) calendar clustering should not be a problem. It can arise when the wrong asset pricing model or a model which permits cross-sectional dependence of the errors is used. We show, that when all events occur on the same day, our tests continue to be well specified. 

·          

3.    Konsep Non-trading effect

·         Solibakke (2002), generally, especially in thinly traded markets, reported closing prices for individual assets do not occur at the same time each day because of non trading. This non-trading effect induce potentially serious biases in the moments and co-moments of asset returns.

4.    Konsep residual risk / homoscedasticity

·         Solibakke (2002), theory might also imply an increase of residual risk during a event period.  Homoscedasticity of the residuals, i.e. their distribution show constant variance, may therefore be strongly disputed.

·         Solibakke (2002), if Homoscedasticity is not the case then standard methodology for measuring the effect of a specific event on security prices, have to be adjusted to take into account the presence of heteroscedasticity.

·         Solibakke (2002), presence of time dependence in stock return series which, if not explicitly treated, will lead to inefficient parameter estimates and inconsistent test statistics. …… these effect in thinly traded markets. 

5.    Konsep asymmetric volatility

·         Solibakke (2002), asymmetric volatility controls for the “leverage effect”. The asymmetric may change in periods where the information flow is high relative to more normal periods. The effect may be more severe in event periods due to higher sensitivity to negative news as for example announcement from the authorities that they will oppose the merger or acquisition. Consequently, we examine  the impact of correcting the market model applying ARMA-GARCH LAG specifications for bivariate time series estimations. (ARMA model is applied for the conditional means and the GARCH model is applied for the conditional volatility. ARCH/GARCH methodology was first introduced by Engle in 1982 dan refined and extended by Bollerslev in 1986 and 1987. Engle and Kroner Extended the models to the multivariate case in 1995.

·         Solibakke (2002), trading on for example asymmetric information may produce price change and will probably increase the volatility of the asset.

6.    Konsep Event and non-event period : time line

·         Solibakke (2002), dalam time line untuk event study dapat digambarkan sebagai berikut :

ESTIMATION PERIOD

EVENT PERIOD

tb

tpre

tc

tpost

Gambar …… Time Line dalam Event Study for merger and Aquisitions Sumber : Solibakke Per Bjarte (2002) dalam artikelnya  tentang Calculating abnormal returns in event studies: Controlling for non-synchronous trading and volatility clustering in thinly traded markets, dalam Managerial Finance; 2002; 28, 8; pg. 72

 

Keterangan :

·         T_b is the first period used in the estimations of a normal security return

·         T_pre is the first period used in the calculation of abnormal return

·         T_c is the event date

·         T_post is the last period use in the calculation of abnormal return.

·         Solibakke (2002), in the literature we usually find a selection of t_pre equal to -40 days to t_c . The length of the estimation period is a weight of benefit of a longer period and the cost of a longer period. Usually, we find a choice from 12 to 14 month prior to the event announcement ( t_c). hence, there are from 230 to 270 daily return observation.

·         s

7.    Konsep long vs short horizon event study

·         Solibakke (2002), dalam time line untuk event study dapat digambarkan sebagai berikut :

·         Kothari and  Warner (1997), long horizon test focusing on pre-event periods are important for understanding whether unusual performance preceded or caused an event. Test for post-event abnormal return provide evidence on market efficiency.

·         Kothari and Warner (2004), Table 1 makes no distinction between long horizon and short horizon studies. While the exact definition of “long horizon” is arbitrary, it generally applies to event windows of 1 year or more. Approximately 200 of the 565 event studies listed in Table 1 use a maximum window length of 12 months or more, with no obvious time trend in the year by year proportion of studies reporting a long-horizon result.

·         Kelemahan long term horizon event study, Kothari and Warner (2004),While long-horizon methods have improved, serious limitations of long-horizon methods have been brought to light and still remain. We now know that inferences from long-horizon tests “require extreme caution” (Kothari and Warner, 1997, p. 301) and even using the best methods “the analysis of long-run abnormal returns is treacherous” (Lyon, Barber, and Tsai, 1999, p. 165). These developments underscore and dramatically strengthen earlier warnings (e.g., Brown and Warner, 1980, p. 225) about the reliability – or lack of reliability - of long-horizon methods. This contrasts with short-horizon methods, which are relatively straightforward and trouble-free. As a result, we can have more confidence and put more weight on the results of short-horizon tests than long- horizon tests. Short-horizon tests represent the “cleanest evidence we have on efficiency” (Fama, 1991, p.1602), but the interpretation of long-horizon results is problematic. As discussed later, long-horizon tests are highly susceptible to the joint-test problem (see sections 3.4 and 3.5), and have lower power.

·         Kothari and Warner (2004), short-horizon event study methods are generally well-specified, but long-horizon methods are sometimes very poorly specified. …. short-horizon methods are quite powerful if (but only if) the abnormal performance is concentrated in the event window. For example, a precise event date is known for earnings announcements, but insider trading events might be known to have occurred only sometime during a one-month window. In contrast to the short-horizon tests, long- horizon event studies (even when they are well-specified) generally have low power to detect abnormal performance, both when it is concentrated in the event window and when it is not. That power to detect a given level of abnormal performance is decreasing in horizon length is not surprising, but the empirical magnitudes are dramatic.

·         Kothari and Warner (2004), a common problem shared by both short- and long-horizon studies is that when the variance of a security’s abnormal returns conditional on the event increases, test statistics can easily be misspecified, and reject the null hypothesis too often.

·         Solibakke (2002), the estimation and event period is studied simultaneously and the investigation control for non-synchronous trading, volatility clustering and asymmetric volatility over both the estimation and the event period.

·          

4. Long-Horizon Event Studies

·         Kothari and Warner (2004)All event studies, regardless of horizon length, must deal with several basic issues. These include risk adjustment and expected/abnormal return modeling (Section 4.2), the aggregation of security-specific abnormal returns (Section 4.3), and the calibration of the statistical significance of abnormal returns (Section 4.4). These issues become critically important with long horizons. The remainder of this chapter focuses on efforts in the long-horizon literature to deal with the issues.

·         Kothari and Warner (2004), Long-horizon event studies have a long history, including the original stock split event study by Fama, Fisher, Jensen, and Roll (1969). As evidence inconsistent with the efficient markets hypothesis started to accumulate in the late seventies and early eighties, interest in long-horizon studies continued. Evidence on the post-earnings announcement effect (see Ball and Brown, 1968, and Jones and Litzenberger, 1970), size effect (Banz, 1981), and earnings yield effect (Basu, 1977 and 1983) contributed to skepticism about the CAPM as well as market efficiency. This evidence prompted researchers to develop hypotheses about market inefficiency stemming from investors’ information processing biases (see DeBondt and Thaler, 1985 and 1987) and limits to arbitrage (see DeLong et al., 1990a and 1990b, and Shleifer and Vishny, 1997). (kegunaan long term horizon)

·         Kothari and Warner (2004), The “anomalies” literature and the attempts to model the anomalies as market inefficiencies has led to a burgeoning field known as behavioral finance. Research in this field formalizes (and tests) the security pricing implications of investors’ information processing biases.⁹ Because the behavioral biases might be persistent and arbitrage forces might take a long time to correct the mispricing, a vast body of literature hypothesizes and studies abnormal performance over long horizons of one-to-five years following a wide range of corporate events. The events might be one-time(unpredictable) phenomena like an initial public offering or a seasoned equity offering, or they may be recurring events such as earnings announcements.

·         Gershgoren (2006),  Long run event studies, which have been used to examine the price behavior of equity for periods of one to five years following significant corporate events (e.g. IPOs, SEOs, repurchases, bond rating changes, etc.) are an increasingly important part of the finance literature.

·         Gershgoren (2006),   Despite considerable interest in the long-run behavior of prices relative to expectations, finance scholars continue to search for an appropriate technique for hypothesis testing. There are two basic issues debated in the literature. The first is how to measure long-run abnormal performance, and the second concerns the appropriate statistical methodology to test for the significance of the performance.

·         Gershgoren (2006),  Here we develop a well-specified and powerful test for long-run abnormal performance as measured by the buy and hold abnormal return (BHAR); defined as the difference between the long-run return for a sample asset and a benchmark selected to capture expected return. We take as given the position (as argued by Barber and Lyon (1997) for example, see Fama (1998) for an alternative view) that the appropriate measure of long-run performance is the BHAR rather than the long-run cumulative abnormal return (CAR). At the heart of this argument is the recognition that the BHAR provides a measure of long-run investor experience, whereas the CAR instead measures average periodic performance, and as such is a biased estimator of investor experience. 

·         Gershgoren (2006),  The more serious problem associated with the use of a reference portfolio to capture expected return is the skewness bias. This bias arises because the long- run return of a portfolio is compared to the long-run return of an individual asset. The long-run holding-period return of an individual security (commonly a samplefirm’s equity) is highly skewed; whereas the long-run holding-period return for a reference portfolio (due to diversification) is not. Consequently, the BHAR, the difference between these returns, also has a skewed distribution. Barber and Lyon demonstrate in simulations that the BHAR ’s positive skewness causes standard tests to have the wrong size (the null hypothesis to be rejected too often when it is true, see also Kothari and Warner (1997)) and causes the power of the test to be asymmetric—rejection rates are far higher when induced abnormal returns are negative than when they are positive.

·         Kothari and  Warner (1997), a rapidly growing literatures suggest delayed stock price reaction to least  a dozen events, with abnormal performance apparently persisting for years following events. As surveyed later, the events include : repurchase tender offers (Lakonishok and Vermaelen , 1983), spinoffs (Cusatis, Miles and Woolridge, 1993; Hite and Owers, 1983), dividend initiations (michaely , Thaler and Womack, 1995),

6. Skewness

·         Kothari and Warner (2004), Long-horizon buy-and-hold returns, even after adjusting for the performance of a matched firm (or portfolio), tend to be right skewed. The right skewness of buy-and-hold returns is not surprising because the lower bound is -100% and returns are unbounded on the upside. Skewness in abnormal returns imparts a skewness bias to long-horizon abnormal performance test statistics (see Barber and Lyon, 1997). Brav (2000, p. 1981) concludes that “with a skewed-right distribution of abnormal returns, the Student t- distribution is asymmetric with a mean smaller than the zero null.” While the right- skewness of individual firms’ long-horizon returns is undoubtedly true, the extent of skewness bias in the test statistic for the hypothesis that mean abnormal performance for the portfolio of event firms is zero is expected to decline with sample size.¹⁵ Fortunately, the sample size in long-horizon event studies is often several hundred observations (e.g., Teoh, Welch, and Wong, 1998, and Byun and Rozeff, 2003). Therefore, if the BHAR observations for the sample firms are truly independent, as assumed in using a t-test, the Central Limit Theorem’s implication that “the sum of a large number of independent random variables has a distribution that is approximately normal” should apply (Ross, 1976, p. 252). The right-skewness of the distribution of long-horizon abnormal returns on event portfolios, as documented in, for example, Brav (2000) and Mitchell and Stafford (2000), appears to be due largely to the lack of independence arising from overlapping long-horizon return observations in event portfolios. That is, skewness in portfolio returns is in part a by-product of cross-correlated data rather than a direct consequence of skewed firm-level buy-and-hold abnormal (or raw) returns.

4.4.2 Cross-correlation

·         The issue. Specification bias arising due to cross-correlation in returns is a serious problem in long-horizon tests of price performance. Brav (2000, p. 1979) attributes the misspecification to the fact that researchers conducting long-horizon tests typically “maintain the standard assumptions that abnormal returns are independent and

·         15 Simulation evidence in Barber and Lyon (1997) on skewness bias is based on samples consisting of 50 firms and early concern over skewness bias as examined in Neyman and Pearson (1928) and Pearson (1929a and 1929b) also refers to skewness bias in small samples.

·         normally distributed although these assumptions fail to hold even approximately at long horizons.”¹⁶ The notion that that economy-wide and industry-specific factors would generate contemporaneous co-movements in security returns is the cornerstone of portfolio theory and is economically intuitive and empirically compelling. Interestingly, the cross-dependence, although muted, is also observed in risk-adjusted returns.¹⁷ The degree of cross-dependence decreases in the effectiveness of the risk-adjustment approach and increases in the homogeneity of the sample firms examined (e.g., sample firms clustered in one industry). Cross-correlation in abnormal returns is largely irrelevant in short-window event studies when the event is not clustered in calendar time. However, in long-horizon event studies, even if the event is not clustered in calendar time, cross-correlation in abnormal returns cannot be ignored (see Brav, 2000, Mitchell and Stafford, 2000, and Jegadeesh and Karceski, 2004). Long-horizon abnormal returns tend to be cross-correlated because: (i) abnormal returns for subsets of the sample firms are likely to share a common calendar period due to the long measurement period; (ii) corporate events like mergers and share repurchases exhibit waves (for rational economic reasons as well as opportunistic actions on the part of the shareholders and/or management); and (iii) some industries might be over-represented in the event sample (e.g., merger activity among technology stocks).

·         If the test statistic in an event study is calculated ignoring cross-dependence in data, even a fairly small amount of cross-correlation in data will lead to serious

·         16 Also see Barber and Lyon (1997), Kothari and Warner (1997), Fama (1998), Lyon, Barber, and Tsai (1999), Mitchell and Stafford (2000), and Jegadeesh and Karaceski (2004).

·         17 See Schipper and Thompson (1983), Collins and Dent (1984), Sefcik and Thompson (1986), Bernard (1987), Mitchell and Stafford (2000), Brav (2000), and Jegadeesh and Karceski (2004).

·         misspecification of the test. In particular, the test will reject the null of no effect far more often than the size of the test (see Collins and Dent, 1984, Bernard, 1987, and Mitchell and Stafford, 2000). The overrejection is caused by the downward biased estimate of the standard deviation of the cross-sectional distribution of buy-and-hold abnormal returns for the event sample of firms.

·         Potential solutions. One simple solution to the potential bias due to cross- correlation is to use the Jensen-alpha approach. It is immune to the bias arising from cross-correlated (abnormal) returns because of the use of calendar-time portfolios. Whatever the correlation among security returns, the event portfolio’s time series of returns in calendar time accounts for that correlation. That is, the variability of portfolio returns is influenced by the cross-correlation in the data. The statistical significance of the Jensen alpha is based on the time-series variability of the portfolio return residuals. Since returns in an efficient market are serially (almost) uncorrelated, on this basis the independence assumption in calculating the standard error and the t-statistic for the regression intercept (i.e., the Jensen alpha) seems quite appropriate. However, the

·         evidence is that this method is misspecified in nonrandom samples (Lyon et al., 1999, Table 10). This is unfortunate, given that the method seems simple and direct. The reasons for the misspecification are unclear (see Lyon et al.). Appropriate calibration under calendar time methods probably warrants further investigation.

·         In the BHAR approach, estimating standard errors that account for the cross- correlation in long-horizon abnormal returns is not straightforward. As detailed below, there has been much discussion, and some interesting progress. Statistically precise estimates of pairwise cross-correlations are difficult to come by for the lack of availability of many time-series observations of long-horizon returns to accurately estimate the correlations (see Bernard, 1987). The difficulty is exacerbated by the fact that the only a portion of the post-event-period might overlap with other firms. Researchers have developed bootstrap and pseudoportfolio-based statistical tests that might account for the cross-correlations and lead to accurate inferences.

·         Cross-correlation and skewness. Lyon et al. (1999) develop a bootstrapped skewness-adjusted t-statistic to address the cross-correlation and skewness biases. The first step in the calculation is the skewness-adjusted t-statistic (see Johnson, 1978). This statistic adjusts the usual t-statistic by two terms that are a function of the skewness of the distribution of abnormal returns (see eq. 5 in Lyon et al., 1999, p. 174). Notwithstanding the skewness adjustment, the adjusted t- statistic indicates overrejection of the null and thus warrants a further refinement. The second step, therefore, is to construct a bootstrapped distribution of the skewness-adjusted t-statistic (see Sutton, 1993, and Lyon et al., 1999). To bootstrap the distribution, a researcher must draw a large number (e.g., 1,000) of resamples from the original sample of abnormal returns and calculate the

·         skewness-adjsuted t-statistic using each resample. The resulting empirical distribution of the test statistics is used to ascertain whether the skewness-adjusted t- statistic for the original event sample falls in the á% tails of the distribution to reject the null hypothesis of zero abnormal performance.

·         The pseudoportfolio-based statistical tests infer statistical significance of the event sample’s abnormal performance by calibrating against an empirical distribution of abnormal performance constructed using repeatedly-sampled pseudoportfolios.¹⁸ The empirical distribution of average abnormal returns on the pseudoportfolios is under the

·         null hypothesis of zero abnormal performance. The empirical distribution is generated by repeatedly constructing matched firm samples with replacement. The matching is on the basis of characteristics thought to be correlated with the expected rate of return. Following the Fama and French (1993) three-factor model, matching on size and book­to-market as expected return determinants is quite common (e.g., Lyon et al., 1999, Byun and Rozeff, 2003, and Gompers and Lerner, 2003). For each matched-sample portfolio, an average buy-and-hold abnormal performance is calculated as the raw return minus the benchmark portfolio return. It’s quite common to use 1,000 to 5,000 resampled portfolios to construct the empirical distribution of the average abnormal returns on the matched-firm samples. This distribution yields empirical 5 and 95% cut-off probabilities against which the event-firm sample’s performance is calibrated to infer whether or not the event-firm portfolio buy-and-hold abnormal return is statistically significant.

·         18 See, for example, Brock, Lakonishok, and LeBaron (1992), Ikenberry, Lakonishok, and Vermaelen (1995), Ikenberry, Rankine, and Stice (1996), Lee (1997), Lyon, Barber, and Tsai (1999), Mitchell and Stafford (2000), and Byun and Rozeff (2003).

·         Unfortunately, the two approaches described above, which are aimed at correcting the bias in standard errors due to cross-correlated data, are not quite successful in their intended objective. Lyon et al. find pervasive test misspecification in non­random samples. Because the sample of firms experiencing a corporate event is not selected randomly by the researcher, correcting for the bias in the standard errors stemming from the non-randomness of the event sample selection is not easy. In a strident criticism of the use of bootstrap- and pseudoportfolio-based tests, Mitchell and Stafford (2000, p. 307) conclude that long-term event studies often incorrectly “claim that bootstrapping solves all dependence problems. However, that claim is not valid. Event samples are clearly different from random samples. Event firms have chosen to participate in a major corporate action, while nonevent firms have chosen to abstain from the action. An empirical distribution created by randomly selecting firms with similar size-BE/ME characteristics does not replicate the covariance structure underlying the original event sample. In fact, the typical bootstrapping approach does not even capture the cross-sectional correlation structure related to industry effects....” Jegadeesh and Karceski (2004, pp. 1-2) also note that the Lyon et al. (1999) approach is misspecified because it “assumes that the observations are cross-sectionally uncorrelated. This assumption holds in random samples of event firms, but is violated in nonrandom samples. In nonrandom samples where the returns for event firms are positively correlated, the variability of the test statistics is larger than in a random sample.

·         Therefore, if the empiricist calibrates the distribution of the test statistics in random samples and uses the empirical cutoff points for nonrandom samples, the tests reject the null hypothesis of no abnormal performance too often.”

·         Autocorrelation. To overcome the weaknesses in prior tests, Jegadeesh and Karaceski (2004) propose a correlation and heteroskedasticity- consistent test. The key innovation in their approach is to estimate the cross-correlations using a monthly time- series of portfolio long-horizon returns (see Jegadeesh and Karceski, 2004, section II.A for details). Because the series is monthly, but the monthly observations contain long- horizon returns, the time-series exhibits autocorrelation that is due to overlapping return data. The autocorrelation is, of course, due to cross-correlation in return data. The autocorrelation is expected to be positive for H-1 lags, where H is the number of months in the long horizon. The length of the time-series of monthly observations depends on the sample period during which corporate events being examined take place. Because of autocorrelation in the time series of monthly observations, the usual t- statistic that is a ratio of the average abnormal return to the standard deviation of the time series of the monthly observations would be understated. To obtain an unbiased t- statistic, the covariances (i.e., the variance-covariance matrix) should be taken into account. Jegadeesh and Karceski (2004) use the Hansen and Hodrick (1980) estimator of the variance-covariance matrix assuming homoskedasticity. They also use a heteroskedasticity-consistent estimator that “generalizes White’s heteroskedasticity­consistent estimator and allows for serial covariances to be non-zero” (p. 8). In both random and non-random (industry) samples the Jegadeesh and Karceski (2004) tests perform quite well, and we believe these might be the most appropriate to reduce misspecification in tests of long-horizon event studies.

·         4.4.3 The bottom line

·         Despite positive developments in BHAR calibration methods, two general long- horizon problems remain. The first concerns power. Jegadeesh and Karceski report that their tests show no increase in power relative to that of the test employed in previous research, which already had low power. For example, even with seemingly huge cumulative abnormal performance (25% over 5 years) in a sample of 200 firms, the rejection rate of the null is typically under 50% (see their Table 6).

·         Second, as discussed earlier (Section 3.6), events are generally likely to be associated with variance increases, which are equivalent to abnormal returns varying across sample securities. Previous literature shows that variance increases induce misspecification, and can cause the null hypothesis to be rejected far too often. Thus, whether a high level of measured abnormal performance is due to chance or misp ricing (or a bad model) is still difficult to empirically determine, unless the test statistic is adjusted downward to reflect the variance shift. Solutions to the variance shift issue include such intuitive procedures as forming subsamples with common characteristics related to the level of abnormal performance (e.g., earnings increase vs. decrease subsamples). With smaller subsamples, however, specification issues unrelated to variance shifts become more relevant.

·         Given the various power and specification issues, a challenge that remains for the profession is to continue to refine long-horizon methods. Whether calendar time, BHAR methods or some combination can best address long-horizon issues remains an open question.

tahapan dalam event study

·         Thompson (1985), the event study problem is broken down into three  phases : (1) the parameterization of information arrival applicable to the problem (2) an examination of the relationship between parameters in the information arrival process and  estimates resulting from alternative estimation methods (3) aggregation across firms experience similar events. Tahap 1 : an attempt is made to formulate a security return-generating process that parameterizes the event study problem. The process is conditioned on the existence or absence of the event under study. Tahap 2 : is exemplified by performance such as a comparison with in the confines of a specified model of information arrival.

Menghitung expected return

Chu (2004), berpendapat bahwa mengukur abnormal return dapat ditempuh dengan berbagai metode antara lain :

Mean Adjusted Model

The simplest model for determining normal returns is the mean adjusted model. This model assumes that the ex ante normal return for a given security i is equal to a constant, i.e

E[R K , which can differ across securities. Predicted ex post return in time t is equal to K .

Abnormal return (AR_IL) for a given event is calculated by subtracting K. from security's return during event period, i.e.

AR_u= R_u — K.                                                                                         (3.1)

Market Adjusted Model

This model assumes ex ante expected returns are equal across securities but not necessarily constant over time. As market portfolio is an average of all available securities, predicted ex post return in time t is equal return from the market Abnormal return (AR, ) for a given event is calculated by subtracting R_m, from security's return during event period, i.e.

ARit =            R_mt                                                           (3.2)

Market Model

This model assumes ex ante expected return for a security is linear function of a common

(market) factor - return from market portfolio, i.e.

E[R_i]. a_i + AR_AI                                                              (3.3)

where a _i and are constant for a given security. Predicted ex post return in time t assumes the

same relation.

Abnormal return (AR_if) for a given event is calculated by subtracting predicted ex post return from security's actual return during event period, i.e.

AR_i,_t = Rr,r — (a, + _Pi R_m,_f)                                                                   (3.4)

where a, and A are estimates of (x_i and A, respectively.

Multifactor Models

Market model (3.3), as well as CAPM, uses a single factor, fi , to control for the risk of a
stock's return associated with the market as a whole. Several researchers argue that the risks with
a stock go beyond the market return, and other common factors exist and are priced by the market.
This group of models assumes ex ante expected return for a security is a linear function of

two or more variables, i.e.

E[R_i]= y_oi + r_uX_i + • y_niX „                                              (3.5)

where v v

, of , • ' • rni are constant for a given security. Predicted ex post return in time t assumes the same relation.

Abnormal return (ARO for a given event is calculated by subtracting predicted ex post return from security's actual return during event period, i.e.

= Ri t — (j? ₀, + „X + • • • p_nix„,,)                  (3.6)

where P_ki is estimated value of y_u , k = 0,1, • • • n .

One of the best-known multifactor models is the 3-factor model developed by Fama and French (1992). Fama and French (1992) started with the observation that two classes of stocks have tended to do better than the market as a whole: (i) small caps and (ii) stocks with a high book-to-market ratio (customarily called "value" stocks; their opposites are called "growth" stocks). By including Size (market capitalization) and Value (book-to-market ratio) along with the excess return from the market, many CAPM anomalies can be explained³. Fama and French claim the anomalies documented in the literature are due to inadequate measures of risk by Beta. They interpret the positive return to Size and Value as risk premium, and state "SMB and HML mimic combinations of two underlying risk factors or state variables of special hedging concern to investors" (Fama and French, 1996).

Two factors are added to CAPM to reflect a stock's exposure to missing non-market risks:

         R1 _=(R,nt— R₁) + b₂,SMB₁₁ + b₃₁HML„ +                        (3.7)

Here R. is the stock i's return at time t, R_I is the risk-free return rate, and R., is time t return of market. SMB„ and HML„ measure the historical excess returns of small capitalized

stocks and "value" stocks over the market as a whole. By the way SMB and HML are defined, the
corresponding coefficients b_2i and b₃₁ take values on a scale of roughly 0 to 1: b_2i = 1 would be a

small cap portfolio, b₂₁= 0 would be large cap, and b_3i = 1 would be a portfolio with a high book/market ratio, etc

Compared to market model, mean-adjusted and market-adjusted models are at best only slightly simpler. Chandra, Moriarty and Willinger (1990) showed that if the market model is the true normal return generating process, abnormal return estimated with mean-adjusted model

equals that estimated with market model plus the product of      and the difference between

actual and expected return from market portfolio. If market return is higher (lower) than its expectation during, abnormal return calculated with mean-adjusted model will be positively (negatively) biased. While the bias will average out if large sample is available, additional noise in abnormal return estimator due to disturbance in market return will not disappear.

Market-adjusted model is simpler than market model in which no statistical parameters are estimated. If market model is the correct return generating process, abnormal return estimated

with market-adjusted model equals that estimated with market model plus a, and the product of
market return R_m, and fi_i —1, therefore is biased. The bias will average out in large sample if
the mean intercept is zero and if average event period market returns is zero, or if average /3 for

the sample is one. Additional noise is added to due to variation in market return, but it will be much smaller than that added by using mean-adjusted model.

Market model controls for the risk (market factor) of the stock and the variation of the market during the event period. Market model resemble one-factor equilibrium model such as Sharpe-Lintner CAPM in that a security's return is assumed to be composed of two parts: one that can be diversified away (systematic risk, as measured by /3 ), and one that can not (unsystematic

risk). It can be shown that if the CAPM is the true return generating process, fi in the market

model equals the Beta coefficient in CAPM, and the intercept in the market model is a, (^1— fli)Rf,t where R_f., is time t risk free rate of return.

If CAPM is the true return generating process and market model is used as the benchmark that estimated with CAPM plus (1 — /3_i)(R_fa                                        , where R₁ is the average value of the risk

free rate. While this bias will average out in large sample when average sample Beta equals one, abnormal return estimated with market model will be noisier than the CAPM estimator.

Finally, as with CAPM, abnormal return estimator with market model is biased if normal return is generated by a multifactor model. When one factor is return of market portfolio, the bias will average out in large sample, however, the abnormal return estimator will be noisier than multifactor model estimator.

Statistical Power of Event Study Models

Studies comparing the relative performance of return generating models include Brown and Warner (1980, 1985), Chandra, Moriarty and Willinger (1990), Dyckman, Philbrick and Stephen (1984), Brown and Weinstein (1985) and others. Brown and Warner (1980, 1985) compare powers of three normal return generating models: mean-adjusted model, market-adjusted model, and market model. They concluded (1980) that, with monthly return data, mean-adjusted model picks up abnormal performance as frequently as market-adjusted model and market model when there is no event time clustering, and that the power of test using market model is not enhanced by choice of risk adjustments. Adding to these, they also concluded (1985) that, with daily return data, tests adjusting for cross-sectional dependencies among returns are not necessary, and actually harmful.

Chandra, Moriarty and Willinger (1990) argue that Brown and Warner's (1980, 1985) findings of superiority for mean-adjusted model is a result of using non-comparable tests (i.e. Brown and Warner used I'atell-test for mean-adjusted model and conventional t-test for market- adjusted model and market model). Using consistent testing methodologies for the three models, Chandra et al. reported that market-adjusted model and market model are more powerful than mean-adjusted model, and it is necessary to use tests which account for cross-sectional dependencies

Dyckman, Philbrick, and Stephen (1984) compare the relative performance of mean- adjusted model, market-adjusted model, and market models in detecting abnormal performance. Their findings suggest there is no significant difference between mean-adjusted model and market-adjusted model. However market model performs significantly better. Brenner (1979) tests market-adjusted model and market model. Small but significant difference is found in the tests of cumulative abnormal returns the two models. Market model dominates the implementation of the market-adjusted model. Furthermore, market model is generally equivalent to the more complicated market index model such as CAPM.

Brown and Weinstein (1985) examine the power of multifactor models in the event studies. In general, statistical properties of residuals from multifactor model regressions appear very similar to those from market model. Given that residuals from market model are noisier when security returns are generated by multifactor models, tests with multifactor model are more powerful. However, Brown and Weinstein (1985) found only marginal improvement when multifactor model is applied. Furthermore, Brown and Weinstein argued that if the factors beyond the market return have little explanatory power or the coefficients are imprecisely estimated, the market model may even perform better in practice.

Besides the model specifications, power of event study methods depends on potential problems such as uncertainty about event dates, non-normality of security returns, event time clustering etc. Also most normal return generating models (e.g. market model, CAPM, multifactor models, etc) are estimated with OLS technique. OLS estimation requires security return to be normally distributed with constant variance in order to achieve best unbiased estimator. Furthermore, security returns should not be correlated over time or across firms. Violations of any of these assumptions will permit other estimators to outperform OLS

Autocorrelation in the residuals of the market model (or multifactor models) render OLS inefficient. Scholes and Willians (1977) provide an alternative estimation procedure for serial correlation introduced by the non-synchronous trading often present in the NASDAQ market and daily stock return. The modifications, however, provide only marginal improvements at best in event study (Dyckman, Philbrick and Stephen (1984), Brown and Warner (1985), and Campbell and Wasley (1993)).

Brown and Warner (1985) also find misspecification may result due to event induced variance increase. Collins and Dent (1984) derive a generalized least square (GLS) procedure which copes with this as well as the correlation of residuals resulting from event date clustering. Schipper and Thompson (1983), Binder (1985) and Thompson (1985) support GLS procedure. Malatesta (1986), McDonald (1987) and Karafiath (1994), however, provide simulation evidence that gains from GLS estimation are minimal and recommend the use of the simpler OLS procedure.

Overall, previous literature suggests the event study methodology is, with corrections for statistical problems that rise in certain scenarios, a powerful tool in detecting event related information. When events are from unrelated industries and when event dates are not clustered, a single factor market model will work at least as well as other models in generating normal return