Hello,

I am currently conducting an event study. I used the Stata code eventstudy2 by Mr. Kaspereit and everything worked wonderfully after I also solved the problem with "nearmrg" as described in the statalist forum (https://www.statalist.org/forums/for...ng-eventstudy2).

However, I am still stumbling a bit over the use of log returns. I have used discrete returns as input and the results have then been automatically converted to continuously compounded returns ("log returns") by the internal conversion of eventstudy2 when executing the command. Thus, the output is also based on continuously compounded returns. I am mainly interested in the respective cumulative abnormal returns (CARs) for the individual events of my event study (i.e. the cross file).

Can someone explain to me (1) why continuously compounded returns ("log returns") are used at all? Mr. Kaspereit says in the statalist forum: "Consequently, the output is also based on continuously compounded returns. For good reasons, this cannot be changed."
(2) Does the use of continuously compounded returns ("log returns") change anything in the interpretation of the abnormal returns?
(3) Or does the interpretation of the coefficients in a regression change, e.g., if the CARs are the dependent or independent variable?

(4) Regarding my study, the mean of the CARs in my sample is -0.0009. Can I still convert this mean from continuously compounded to discrete? Or can I also convert each CAR in the cross file, i.e. the CAR for each separate event? For the example above, the formula should be: discrete return = e^(-0.0009)-1 = -0.0008995. As far as I know, the mean of the CARs of -0.0009 (-0.09%) should then be seen as an average reduction of firm value by -0.0008995 (-0.08995%). Many event studies use continuously compounded returns ("log returns"), but do not elaborate on why they are used. I also do not see any differences in the interpretation of the results in the academic literature. Only in one article I have seen an interpretation like the one I gave above (Salinger, M. 1992, p. 49: https://www.jstor.org/stable/2331297). (5) Is the use of log returns just about the often discussed better statistical properties or what is the use of log returns then about?

I hope you can help me with my interpretation difficulties and questions (denoted in brackets).

Best regards,
Max