General problems using the event-study approach .1 How important is the length L of the estimation window?

In my study on the merger paradox in the year 1908, I used fifty observations of daily returns starting on 1^st January 1907 of every stock in my sample. To assess the impact of the length of the event window, the number of observations is now doubled. The variance of the estimated mean Var(µˆ) should be reduced by approximately one half if the assumptions regarding normally identically independently distributed daily returns is fulfilled to a high extent. Note that this variance term is in general less important than the variance of the error terms of the constant-mean-return model (CMR) σe2 (see 2.10). After doubling the length of the estimation period, the variance of the estimated normal return Var(µˆ) increased on average by 16.29% – although one should observe the opposite reaction. Accordingly, the i.i.d. assumption imposed on daily returns is far from being true. In addition, the total average increase in the additive variance term is 95.33% because the variance of the error term of the CMR model¹⁰⁰ skyrocket caused by stronger deviations of returns from their estimated mean. Therefore, I

100 See equation (2.4).

conclude that increasing the estimation window does not lead to an improved estimation of the normal return because the range of the normal stock price movement is even larger.

Henceforth, it would be more difficult to detect abnormal share price movements.¹⁰¹

Besides different variances, estimated normal returns may differ considerably; thus, abnormal returns could be severely influenced by the chosen estimation period. For instance, Klein and Rosenfeld (1987) argued that bull or bear markets can bias the estimation of normal returns. Accordingly, I should investigate whether changes regarding the estimation period possess a remarkable impact on normal returns. Sticking to the standard procedure discussed by Levin (1999),¹⁰² I test whether the normal returns based on the period from January to February 1907 differ significantly from the enlarged period that starts in January ending after 100 daily observations. The t-values are generally very small – but in one case out of forty-five the t-value reaches –3.31; however, a considerable distortion of my former results can be ruled out. Note that the exceptional case of `Magdeburger Privatbank´ also shows that using the period from January to February 1907 yields significantly higher normal returns by 0.09 percentage points than choosing the extended period. Consequently, extending the period would in this case lead to higher abnormal returns.

One can also assess whether the mean return deviates for the whole sample of companies if the event period is changed. Consequently, the estimation period from January to February 1907 is replaced by the following two months, March and April 1907. Hotelling’s T-squared reaches 68.47 and the corresponding F-statistic 0.84 (p-value: 0.727); hence, the null hypothesis that mean returns do not differ for all companies cannot be rejected. Based on these results, the choice of the estimation period and its length seem to be of minor importance for my former outcomes.

4.3.2 Is it possible to detect abnormal returns in time periods without events?

Using the estimation period, January to February 1907, with fifty observed daily returns for every stock, I test for abnormal returns by defining the following two month with fifty daily returns as event period. Note that during this defined event period the included firms did not announce any mergers;¹⁰³ thus, one should expect that abnormal returns cannot be detected. In

101 Note that this empirical finding is sample specific and can be explained by the strong decline in share prices from March 1907 to the end of the year 1907.

102Levin (1999) is an excellent introduction into these test procedures. I use a standard test statistic that allows different variances in both estimation periods; thereby, degrees of freedom for the test are obtained from Welch’s approximation formula. Nevertheless, Satterthwaite’s formula yield similar outcomes.

103 One can check this easily by reading the annual information provided by the `Handbuch der deutschen Aktiengesellschaften´; however, very small transactions, e.g. acquisition of another company’s branch in a specific city, are not always reported.

contrast to my former event studies, I use the same event period with respect to the calendar time for every stock in my sample. This procedure uncovers one essential weakness of the event study approach; event studies do not belong to time series methods because event period and calendar time differ.

Furthermore, event studies work best if the event periods of the respective stocks are seldom overlapping. The reason for this finding is straightforward. An event study that is based on event periods that are equal to a specific calendar period cannot distinguish between abnormal returns triggered by remarkable stock specific events and erratic time shocks that usually hit all stock at the same time.¹⁰⁴ Because the inference is usually based on portfolio weighted abnormal returns, a exogenous time shock that affects all stocks in the market at the same point in time causes significant abnormal return.

Overlapping event periods, hence, lead to a so called clustering (see Armitage, 1995) of cross-sectional units. Brown and Warner (1980, 1985) provided empirical evidence of the importance of this problem using Monte Carlo studies. Clustering of observations also leads to cross-correlation of abnormal returns; therefore, critical assumptions imposed to derive my test statistics in chapter two are violated.

Figure 4.1 plots the cumulated portfolio weighted abnormal return of my artificial event period. Even without price-sensitive events on the micro-level, exogenous time shocks caused a significant deviation of current daily returns from their predicted normal stock price movement. In addition, this deviation is only a temporary perturbation.

104 For instance, unexpected macroeconomic shocks. Chapter five discusses this point thoroughly.

Figure 4.1: Time shocks as artificial events

Note that the artificial event period covers 50 days. Besides the portfolio weighted cumulated abnormal return, the upper and lower critical values are plotted. If the cumulated fluctuation process exceeds one of this boundaries, the deviation is recognized as being significant on the 95% level of significance.

-5 -4 -3 -2 -1 0 1 2 3

days of the artificial event period

cumulated abnormal return

4.3.3 Is the constant-mean-return model inferior in comparison to the market model

As mentioned in former chapters, there are indeed good reasons to choose the constant-mean-return model (CMR) to estimate the normal constant-mean-return in historical periods. But for the sample of the year 2000, a market index is easily available; hence, one can prove whether the market model (MM) leads to better estimates than the simple CMR model. Hence, I carry out the stochastic market model¹⁰⁵ that is widely accepted and used nowadays. The daily return of stock i at time t denoted Rit serves as dependent variable, whereas the daily return of the market index DAX30 Rmt enters the equation as explanatory variable. A stock specific constant term is also included. After deriving the normal return, the deviation of current daily returns from its predicted level measures the abnormal performance. To compare the CMR and the MM model, figure 4.2 plots for both versions portfolio weighted abnormal returns.

The differences between these two sequences are negligible; thus, all results obtained in my former studies stay valid if the market model determines the normal stock price movement.

This finding is in line with the simulation experiments of Brown and Warner (1980, 1985).

105 This model version does not impose any further restrictions on the parameters like theoretical market models do (see Dimson and Marsh, 1984). Since Fama et al. (1969) who applied the simple stochastic market model for the first time, it became the most common way to determine normal returns.

Figure 4.2: The `performance´ of the constant-mean-return (CMR) and the stochastic market model (MM)

To evaluate which model outperforms the other, portfolio weighted abnormal returns are calculated based on the CMR or the MM; thereby, I use the sample drawn in 2000.

-2 -1,5 -1 -0,5 0 0,5 1 1,5 2 2,5 3 3,5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

days of the event period

portfolio weighted abnormal return (MM) portfolio weighted abnormal return (CMR)

4.3.4 Do dividend payments affect the results?

During the event period, only one company, namely the mining firm `Laurahütte´, issued a quarterly dividend payment; hence, stock prices on the fifteenth day after the announcement are quoted as ex-dividend prices. In my former event-studies presented in chapter two and three, I worked with these ex dividend stock prices because the dividend payment seems to be negligible. Note that the stock price reached 215 Mark, whereas only a quarter of the annual dividend of 12% with respect to the nominal capital Nit was issued. One method to incorporate dividend payments is to add them to the ex-dividend stock price. This requires to know the day of the issue of dividends. If the date is uncertain, an alternative approach corrects daily returns with regard to annual dividend payments Dit; thereby, one calculates the theoretical daily dividend that should be reflected in current market prices Pit.106

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The difference between the observed daily return Rit and the daily return with embedded dividends RitDiv is relatively low. During the event period the maximum deviation of both time series reaches 0.0255%. Obviously, the impact of dividends becomes more essential if one aggregates daily returns over increasing time intervals. Deriving the cumulated abnormal return for the whole event period with and without controlling for dividends uncovers an aggregated underestimation by neglecting dividends of about 0.1211%. In comparison to the total change of the market value of 2.42%, this underestimation seems acceptable. Besides the distortion during the event period, the estimated normal return is also understated if dividends are not taken into account. In the case of `Laurahütte´, the estimated mean return with adjustments for dividends is 0.0025% higher than without dividends. Hence, the normal return should be 0.0025% higher which diminishes the cumulated abnormal return over the whole event period by 0.0775%. Note that this reduction of cumulated returns caused by higher normal returns is outweighed by the underestimation of cumulated effects of about 0.1211% if dividends are neglected. Therefore, controlling for dividend payments yields to higher cumulated abnormal returns of about 0.0436%. From my point of view, this difference is unimportant and does not justify to spend much time on controlling for dividends.

Furthermore, this example underlines that the rejection of the merger paradox is even more likely if dividends are considered.

106 A similar formula was applied to US and Canadian securities by `Datastream´ until 1973 because detailed information on the exact dates of dividend payments was not accumulated. Accordingly, this method works very well with historical data if one knows only annual dividend payments. Note that I use 260 trading days for this calculation. However, the number of days is not essential for my statements.

Besides this merely technical issue, one should also have in mind the institutional situation during the pre-World-War I period. According to the exchange law of the year 1896,¹⁰⁷ share prices should not reflect `interest rates´ for holding an asset because every shareholder received a 4% annual interest rate payment over the holding period. After the company issued dividends, this prior interest payment are subtracted from dividends. Such pre-payments make a correction for dividends even more complicated and, as discussed above, potential distortions are of minor importance.

4.3.5 Shareholder value orientation versus redistribution theory

Jarrell et al. (1988) highlighted that detecting an increase in market values of acquiring and target firms is certainly not enough to call a merger successful. Obviously, my approach defines a successful transaction as one that maximizes the shareholder value of the involved companies. Only a few empirical studies focused on other stakeholders that could be influenced by mergers, namely employees and bondholders. Nevertheless, the results are ambiguous,¹⁰⁸ and due to a lack of information, I cannot carry out similar studies for the pre-World-War I period.

4.4 Explaining the adaptation process of stock prices: A traditional view