Calculation of short-term bidder returns

The sample selection and event definition for the short-term event study were discussed above. Abnormal return (AR) is the difference between the actual stock return (R) and expected return (E(R)), which is the normal or expected return on the stock during the event window if the acquisition announcement had not taken place. This is calculated using the following formula:

𝐴𝑅𝑖𝑡 = 𝑅𝑖𝑡 − 𝐸(𝑅𝑖𝑡)

Where 𝑖 and 𝑡 denote the security and the day, respectively.

Existing literature on event studies uses a variety of methodologies to estimate benchmark returns (Martynova & Renneboog, 2006). While each model has its own assumptions and its own merits, the choice of the model should be carefully considered. The three main models used to estimate the normal return are mean-adjusted returns, market-adjusted returns and the market model (see Appendix B: Brown & Warner, 1985; Weston et al., 2004). Other models include the factor model and capital asset pricing model (CAPM) (J. Y. Campbell, Lo, & MacKinlay, 1997; Kothari & Warner, 2007).

The market model assumes that there is a linear relationship between the security return and the market return, while the market-adjusted returns model assumes that the expected return of the share is equal to the return of the market and the mean adjusted returns model assumes that the mean return of a given security is constant through time. Logically, it may not be expected that the analysis based on different models can obtain comparable results. However, research suggests that they have similar abilities in detecting abnormal returns (Brown & Warner, 1985; Dyckman, Philbrick, & Stephan, 1984; MacKinlay, 1997). Informed by literature, the present study uses the market model and the market-adjusted returns model to estimate the normal return (see Appendix C).

110

5.5.2.1The market model

The market model takes explicit account of both the risk associated with the market and the mean returns (Kumar & Panneerselvam, 2009). Consistent with prior research studies we estimate the market model expected returns using the formula:

𝐸(𝑅𝑖𝑡 ) = 𝛼𝑖 + 𝛽𝑖𝑅𝑚𝑡

Where, the coefficients 𝛼_𝑖 and 𝛽_𝑖 are regression estimates of the intercept and the slope of

the characteristic line. While 𝑅_𝑚𝑡 is the equal-weighted market return on day 𝑡 of the Shanghai or Shenzhen Stock Exchange depending on which exchange the bidder firm is listed. This is because there is no single composite index for both exchanges. For each stock exchange, we take the All A-Share market returns. These returns are obtained from CSMAR database.

To compute the abnormal returns, firm-specific parameters 𝛼𝑖 and 𝛽𝑖 are estimated with an

OLS regression using 200 daily returns over period starting from event day -220 to event day-21. This is consistent with recommendations made by Bartholdy et al. (2007) that the standard estimation period is between 200 and 250 daily returns (p. 228).

5.5.2.2Aggregation of abnormal returns

Next, to draw inferences for the event window the abnormal return observations are aggregated. The aggregation is along two dimensions, through time for an individual event and both across events and through time for several events.

5.5.2.3Aggregation through time

The first dimension is to aggregate abnormal returns through time for an individual event and to obtain cumulative abnormal returns for the individual event over an event window. For the purposes of this thesis the process is described as follows:

𝐶𝐴𝑅_{𝑖𝑡[−5,+5]} = ∑ 𝐴𝑅_𝑖𝑡

+5

−5

𝐶𝐴𝑅𝑖𝑡[−5,+5], is the cumulative abnormal return for event 𝑖from day (-5) to, day (+5). Day

(-5) is the start of the event window and day(+5) is the end of the event window. Given a sample of N events, the cumulative average abnormal return of all events during the event window is the average of the individual event abnormal returns. This described as follows:

111 𝐶𝐴𝐴𝑅𝑖𝑡 = 1 𝑁∑ 𝐶𝐴𝑅𝑖𝑡 +5 −5

5.5.2.4Aggregation across events and through time

The second aggregation of abnormal returns is to aggregate the abnormal returns across events and through time. Daily abnormal returns are averaged across the sample of events to obtain the average abnormal returns (AAR). Given a sample of N events, the AAR of all events on day (t), is the average of the abnormal returns is described as follows:

𝐴𝐴𝑅_𝑖𝑡 = 1

𝑁∑ 𝐴𝑅𝑖𝑡

+5

−5

The elements of this average abnormal return are then aggregated through time using the same approach as described above. Cumulative average abnormal return (CAAR) is therefore defined as the sum of all average abnormal returns during the event window and is described as follows:

𝐶𝐴𝐴𝑅_𝑖𝑡 = 1

𝑁∑ 𝐴𝐴𝑅𝑖𝑡

+5

−5

Positive CAAR indicates that shareholders experience an increase in their own wealth when the event occurs. On the contrary, shareholders experience losses in their own wealth if negative CAAR is generated. The CAAR is then used as the dependent variable to examine whether shareholders of bidder firms gained from M&A. Henderson (1990) reiterates that CAAR13 _{is the widely used measure of abnormal returns and has ‘withstood the test of time’}

(p. 297).

5.5.2.5Significance testing

The test statistic is used to determine whether the abnormal returns are statistically different from zero. The statistical significance of CAR is determined following Dodd and Warner

112 (1983) and employed by Hagendorff and Keasey (2010). Standardised abnormal returns are used to prevent AR with large variances dominating the test. The t-statistic is calculated using the following formula:

𝑡 = 𝐴𝑅̅̅̅̅𝑖𝑡 𝜕𝐴𝑅𝑖𝑡 /√𝑁

Where, 𝐴𝑅̅̅̅̅𝑖𝑡 is the sample mean and 𝜕𝐴𝑅𝑖𝑡 is the cross-sectional sample standard deviation.