Suppose that we wished to conduct an event study on whether acquiring firms experience share price reactions to takeover announcements. For our event study, we will use for our sample the following three acquiring firms: Company X: Merger announcement date January 15, 2016 Company Y: Merger announcement date February 15, 2016, Company Z: Merger announcement date April 10, 2016 Suppose we establish an 11-day testing period for returns around the event dates, the event date plus five days before and five days after. The table below provides our three acquiring firm stock prices during 12-day periods around merger announcement dates. a) Compute one-day returns for each of 11 days for each of the three stocks. Acquiring company daily stock returns, (Pt/Pt-1) 1, are computed as follows

How to calculate the return showing in the right size table?

b) Suppose that we have decided to use the mean adjusted return method to compute excess or abnormal stock returns. Here, we will compute mean daily returns for each security for a period outside our 11-day testing period. Suppose we compute average daily returns and standard deviations for each of the stocks for 180-day periods prior to the testing periods (the raw returns data are not given here). Suppose that we have found normal or expected daily returns along with standard deviations as follows:

Compute excess returns for each stock for each of the 11 days.

c. For each of the 11 days in the analysis, compute average residuals for the three stocks. Then for each day, compute a standard deviation of residuals for the three stocks. Finally, compute normal deviates for each of the 11 dates based on the averages and standard deviations for the three stocks.

How to calculate the Excess return, average, std dev, and normal deviate showing from this table? What formula should I use?

e) Compute cumulative average residuals for each of the 11 dates. f) Compute standard deviations and normal deviates for each of the 11 dates.

How to calculate the cumulative average residuals, std dev, and normal deviate showing from this table? What formula should I use?

Confused about how these numbers are calculated.

Thank you!

(a) Returns Prices Y z Day -6 50.125 50.125 50.25 Z 60.375 60.5 -5 -4 -3 -2 Y 20 20 20.125 20.25 20.375 20.375 21.375 21.25 21.375 21.5 21.375 50.25 50.375 50.25 52.25 52.375 52.25 -1 0.207% -0.413% -0.207% -0.208% 0.208% 0.832% 0 0.000% 0.249% 0.000% 0.249% -0.248% 3.980% 0.239% -0.239% 0.239% 0.239% -0.238% 60.25 60.125 60 60.125 60.625 60.75 60.75 60.875 60.875 60.875 0.000% 0.625% 0.621% 0.617% 0.000% 4.908% -0.585% 0.588% 0.585% -0.581% 0.585% 1 0.206% 0.000% 2 3 52.375 4 52.5 52.375 0.206% 0.000% 0.000% 5 21.5 Standard Deviation 0.00425 Stock Normal Return x 0.000465 Y 0.000520 z 0.000082 0.00637 0.00220 (b) (c) Excess returns (residuals) Normal Deviate Y Z Average Std Dev Day -6 | | -5 0.23 -0.047% 0.203% -4 0.24 -0.052% 0.573% 0.569% 0.565% 0.199% -0.421% -0.216% -0.216% 0.033% 0.118% 0.102% 0.184% -3 0.25 -2 -0.047% 0.202% -0.295% 0.47 0.143% 0.503% 0.413% 0.391% 0.247% 2.113% 0.480% 0.418% - 1 0 3.934% 0.193% -0.052% 4.856% -0.637% 0.536% -0.049% 3.204% -0.082% 0.081% -0.20 1.52 -0.17 0.19 1 2 0.200% 0.823% 0.198% -0.008% 0.198% -0.008% -0.008% 2 -0.285% 3 0.193% 0.195% 1.58 0.308% -0.150% 4 0.533% -0.633% 0.533% 0.192% -0.285% -0.35 0.431% 0.416% 5 5 0.080% 0.19 (f) (e) Cumulative residuals Cumul. Cumul. Cumul. Avg Residual Y Residual z Residual Cumul. Residual X Normal Deviate Day -6 Std Dev -5 -4 -0.05% 0.16% 0.11% 0.31% -3 0.23 0.41 0.33 0.38 0.36 -2 -1 0.20% -0.22% -0.44% -0.65% -0.45% 0.37% 0.57% 0.56% 0.76% 0 -0.05% 0.52% 1.09% 1.66% 1.60% 6.46% 5.82% 6.36% 6.89% 6.26% 6.79% 0.03% 0.15% 0.25% 0.44% 0.39% 3.59% 3.51% 3.59% 3.90% 3.75% 3.83% 0.02% 3.95% 4.14% 3.86% 4.05% 4.24% 3.96% 0.143% 0.372% 0.774% 1.160% 1.078% 3.061% 2.684% 2.909% 3.070% 2.788% 3.028% 1.17 1 2 3 1.31 1.23 1.27 4 0.75% 1.35 5 0.74% 1.27 (a) Returns Prices Y z Day -6 50.125 50.125 50.25 Z 60.375 60.5 -5 -4 -3 -2 Y 20 20 20.125 20.25 20.375 20.375 21.375 21.25 21.375 21.5 21.375 50.25 50.375 50.25 52.25 52.375 52.25 -1 0.207% -0.413% -0.207% -0.208% 0.208% 0.832% 0 0.000% 0.249% 0.000% 0.249% -0.248% 3.980% 0.239% -0.239% 0.239% 0.239% -0.238% 60.25 60.125 60 60.125 60.625 60.75 60.75 60.875 60.875 60.875 0.000% 0.625% 0.621% 0.617% 0.000% 4.908% -0.585% 0.588% 0.585% -0.581% 0.585% 1 0.206% 0.000% 2 3 52.375 4 52.5 52.375 0.206% 0.000% 0.000% 5 21.5 Standard Deviation 0.00425 Stock Normal Return x 0.000465 Y 0.000520 z 0.000082 0.00637 0.00220 (b) (c) Excess returns (residuals) Normal Deviate Y Z Average Std Dev Day -6 | | -5 0.23 -0.047% 0.203% -4 0.24 -0.052% 0.573% 0.569% 0.565% 0.199% -0.421% -0.216% -0.216% 0.033% 0.118% 0.102% 0.184% -3 0.25 -2 -0.047% 0.202% -0.295% 0.47 0.143% 0.503% 0.413% 0.391% 0.247% 2.113% 0.480% 0.418% - 1 0 3.934% 0.193% -0.052% 4.856% -0.637% 0.536% -0.049% 3.204% -0.082% 0.081% -0.20 1.52 -0.17 0.19 1 2 0.200% 0.823% 0.198% -0.008% 0.198% -0.008% -0.008% 2 -0.285% 3 0.193% 0.195% 1.58 0.308% -0.150% 4 0.533% -0.633% 0.533% 0.192% -0.285% -0.35 0.431% 0.416% 5 5 0.080% 0.19 (f) (e) Cumulative residuals Cumul. Cumul. Cumul. Avg Residual Y Residual z Residual Cumul. Residual X Normal Deviate Day -6 Std Dev -5 -4 -0.05% 0.16% 0.11% 0.31% -3 0.23 0.41 0.33 0.38 0.36 -2 -1 0.20% -0.22% -0.44% -0.65% -0.45% 0.37% 0.57% 0.56% 0.76% 0 -0.05% 0.52% 1.09% 1.66% 1.60% 6.46% 5.82% 6.36% 6.89% 6.26% 6.79% 0.03% 0.15% 0.25% 0.44% 0.39% 3.59% 3.51% 3.59% 3.90% 3.75% 3.83% 0.02% 3.95% 4.14% 3.86% 4.05% 4.24% 3.96% 0.143% 0.372% 0.774% 1.160% 1.078% 3.061% 2.684% 2.909% 3.070% 2.788% 3.028% 1.17 1 2 3 1.31 1.23 1.27 4 0.75% 1.35 5 0.74% 1.27