To answer the questions posed in this paper, we apply event study. This involves several steps: data collection, preparation, and calculation of event window size; estimating normal returns; calculating abnormal returns and cumulative abnormal returns; and testing results. Since the Algiers Stock Exchange does not provide daily data, we use monthly data. We define the event date as the month of dividend announcement (t = 0), which may differ from the dividend payment date (Table 2). This process involves carefully examining the information provided by each company to identify the specific date on which the dividend distribution to shareholders was announced. Then we determine the event window and the estimation window. The event window spans 21 months (-10; +10), starting 10 months before the announcement month and extending until 10 months after the announcement month including the announcement month (t = 0) itself.
The estimation window is used to determine the parameters of the yield-generating model, which is then employed to calculate the abnormal profitability during the event period. It precedes the event window. In our study, the length of the estimation window varies across companies due to data availability constraints. Figure 2 illustrates the design of the event period and the estimation period for Alliance Assurances company:
After organizing the sample and determining the event period and estimation period dates, we calculate the sample stock return, Rit, and market return, Rmt, as follows.
$${R_{it}}=\frac{{S{P_{it}} - S{P_{it - 1}}}}{{S{P_{it - 1}}}},$$
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where Rit denotes an actual return of stock i at month t; SPit and SPit−1 are closing prices of stock i at months t and t-1;
$${R_{mt}}=\frac{{dzairinde{x_t} - dzairinde{x_{t - 1}}}}{{dzairinde{x_{t - 1}}}}$$
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where Rmt denotes an actual return of the Algiers Stock Exchange index (dzairindex) at month t; dzairindext - closing Algiers Stock Exchange index at month t; dzairindext−1 - closing Algiers Stock Exchange index at month t-1.
The estimation of abnormal returns for the companies in the sample is based on the market model (Fama et al., 1969), which is widely used in event studies because of its performance and simplicity. According to this model, the expected return \(\widehat {{{R_{it}}}}\) is the result of the following simple regression equation:
$$\widehat {{{R_{it}}}}={\alpha _i}+{\beta _i}{R_{mt}}+{\varepsilon _{it}},$$
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where αi, ßi are coefficients of the model for stock i;\({\varepsilon _{it}}\) - residual error of stock i at month t.
Abnormal return \(\:{\text{A}\text{R}}_{\text{i}\text{t}}\) is defined as the actual return \(\:{\text{R}}_{\text{i}\text{t}}\) minus expected return calculated using the market model:
$$A{R_{it}}={R_{it}} - \widehat {{{R_{it}}}}.$$
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To analyze the price changes of securities around the event date for four companies listed on the Algiers stock exchange, we calculate the average cross-sectional monthly abnormal return as follows:
$$AA{R_t}=\frac{1}{N}\sum\limits_{{i=1}}^{N} {A{R_{it}},}$$
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where AARt denotes an average abnormal return at month t; N - the number of observations in the study sample.
To gauge the comprehensive effect of the examined event over a specific time frame (event window), we can aggregate individual abnormal returns into a cumulative abnormal return. It represents the cumulative impact of all abnormal returns. The cumulative abnormal return (CAR) is calculated as follows:
$$CA{R_{it}}=\sum\limits_{{t={t_1}}}^{{{t_2}}} {A{R_{it}}.}$$
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Finally, cumulative average abnormal returns (CAAR) are calculated as follows:
$$CAA{R_(}_{{{t_1},{t_2})}}=\frac{1}{N}\sum\limits_{{i=1}}^{N} {CA{R_{it}}} .$$
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Cumulative average abnormal return provides a comprehensive measure of the overall impact of an event on stock returns. In particular, if the impact of the event being studied does not occur exactly in the month of the event, then this estimator can be very important.
For statistical tests that can be performed, the null hypothesis confirms that the abnormal return on month t within the event window is equal to zero: \(H0:E(A{R_t})=0.\) This implies that the event in question has no influence on the price of the securities. Assuming that individual abnormal returns during the event period are normally distributed, the t-student parametric test, as applied by Brown and Warner (1980, 1985), is used to measure the impact that may occur on the day (month) of the event as follows:
$$t=\frac{{AA{R_t}}}{{\sigma (AA{R_t})}},$$
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where AARt denotes an average abnormal return at month t, σ(AARt) - standard deviation of average abnormal returns.
The test procedure consists in dividing the sum of the abnormal return of the event period for all securities on the root of the variance of abnormal return, during the estimation period. The preceding equation is thus reproduced according to the formula below:
$$t=\frac{{\frac{1}{N}\sum\limits_{{i=1}}^{N} {A{R_{i0}}} }}{{\frac{1}{N}\sqrt {\sum\limits_{{i=1}}^{N} {\frac{1}{{T - 1}}{{\left( {A{R_{it}} - \sum\limits_{{t=1}}^{T} {\frac{{A{R_{it}}}}{T}} } \right)}^2}} } }},$$
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where ARi0 presents an abnormal return for stock i during the month of the event (t = 0); T – the length of the estimation period.
The second statistical test assesses the overall effect of dividend announcements on the profitability of the securities. This t-test can be applied to one or more sub-periods within the event window, or to the full event period (-10, + 10). To determine the significance of the cumulative average abnormal return (CAAR), we use the following test:
$$t=\frac{{CAA{R_{{T_1},{T_2}}}}}{{{{\left( {{T_2} - {T_1}+1} \right)}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0pt} 2}}}\sigma (AA{R_t})}},$$
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where T1, T2 denote lower and upper limits of the cumulative period.
In addition, we utilize the Beaver test (Beaver, 1968), which complements t-statistic tests that depend on models generating returns. This test assesses the magnitude of variations (abnormal returns) experienced by a security due to the event under examination. The Beaver test applies to all securities in the sample and consists in transforming abnormal returns without considering their signs. This transformation involves calculating the square of each security’s abnormal return. The test is expressed as a ratio:
$${U_{it}}=\frac{{{{\left( {A{R_{it}}} \right)}^2}}}{{{{\left( {\sigma _{{it}}^{2}\left( {1+(\frac{1}{k})+\frac{{{{({R_{mt}} - \overline {{{R_m}}} )}^2}}}{{\sum\nolimits_{1}^{k} {{{({R_{mk}} - \overline {{{R_m}}} )}^2}} }}} \right)} \right)}^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-0pt}\!\lower0.7ex\hbox{$2$}}}}}},$$
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where \(\overline {{{R_m}}}\) is an average market return calculated for the estimated period; k - number of observations in the estimation period; \(\:{{{\sigma\:}}_{\text{i}\text{t}}}^{2}\) - variance of abnormal return for stock i.
If Uit=1, it indicates that the variance observed during the event period is the same as that calculated during the estimation period and that the share price reaction within the event window does not differ significantly from a normal one. If \(\:{\text{U}}_{\text{i}\text{t}}\:>1\) this means that the abnormal return is higher than normal and shows a significant reaction. If \(\:{\text{U}}_{\text{i}\text{t}}\:<1\), then the abnormal return is lower than normal, and the market reaction to the announcement of the event is insignificant.