## Expert Dialog

Question #7: Calculation of Average AR and CAR

I don´t understand how I calculate average AR and CAR. I have 88 companies and 563 events. Do I need to divide AR by N events (563) or by N companies (88)? For example, event 1, is AAR=0,45629/563=0.00081046. What ist he right way to calculate AAR and ACAR? I would be very happy, if you can help me!
day abnormal_return cumulative_abnormal_return
-5 0.45629 2.65503
-4 -0.09955 2.65503
-3 0.41327 2.65503
-2 -0.16353 2.65503
-1 -0.01421 2.65503
0 0.56482 2.65503
1 -0.19816 2.65503
2 1.96007 2.65503
3 0.11497 2.65503
4 0.2138 2.65503
5 -0.59274 2.65503

Yes, AAR and CAAR are mean averages of the respective AR and CAR values as described here: http://www.eventstudytools.com/event-study-methodology. The event study engine of this website will calculate the AAR and CAAR values for you.
Question #6: Calculation of Average AR and CAR

I don´t understand how I calculate average AR and CAR. I have 88 companies and 563 events. Do I need to divide AR by N events (563) or by N companies (88)? For example, event 1, is AAR=0,45629/563=0.00081046. What ist he right way to calculate AAR and ACAR? I would be very happy, if you can help me!
day abnormal_return cumulative_abnormal_return
-5 0.45629 2.65503
-4 -0.09955 2.65503
-3 0.41327 2.65503
-2 -0.16353 2.65503
-1 -0.01421 2.65503
0 0.56482 2.65503
1 -0.19816 2.65503
2 1.96007 2.65503
3 0.11497 2.65503
4 0.2138 2.65503
5 -0.59274 2.65503

Hello,your problem describtion is not precise. What is the source of this value -5 0.45629? Is this the AR of a single firm or the AAR of your firms? What do you want to analyse?Best
Question #5: Enquiry about t-test on CAR

Dear Dr.

Sorry to bother you. I am a Chinese student and I am doing my MSC dissertation. I am conducting an event study in order to figure out the influence of the release of movies. I feel confused about the way to test CAR. I am wondering can I calculate SD (CAR) directly through the STDEV formula in Excel? Further,I am not sure whether the "N"in the formula you provide to calculate standard deviation of AAR also stand for the number of events. Could you please give me some help? Thank you very much.

Have nice day!

ENQI

Hello,As you have N observations with one event each, you can regard N also as the number of events. The standard deviation of CAR is the length of the event window multiplied with the standard deviation of of the abnormal returns in estimation window. The AR in the estimation window can be calculated by the EXCEL function STDEV.Best,Simon
Question #4: Incorrect calculation of Alpha and Beta

Dear Sir,

I believe that the way Alpha and Beta is calculated in the Basis Abnormal Return tool of your website is incorrect. The formula for Alpha should be as follows: Intercept(stock return of firm. return on index) while the ES with excel file that has been provided to give evidence that the results of your event study methodology tool are correct uses Intercept(return on index, stock return of firm). Same goes for Beta.

Could you please clarify this issue.

I hope to hear from you soon.

Dear Mr. Shahzad,Your right. For calculating abnormal returns you use the return of index as independent variable and the return of firm as dependent variable. I corrected the Excel file on http://www.eventstudytools.com/excel. The abnormal return calculation on the significance site were correct.Best,Simon
Question #3: Calculating the alpha and beta parameters.

How to i calculate the beta and alpha parameters in my market model.

You get the alpha and beta parameter of the market model by doing a linear regression on the data in the estimation window. You can do that analysis e.g. with our App.Best,Simon
Question #2: Possible error in the demo work of J-test

Dear Dr Muller,

I am Vineet, a PhD student and who is referring to your demo work in excel for various event study methodology.

I appreciate the work done here and I find it very helpful.

I am currently referring to your work done on J-Test on the following page:
http://www.eventstudytools.com/significance-tests

I tried to replicate the methodology and got different results. I wish to resolve the inconsistencies.

Calculation of average correlation is certainly one problematic area. The paper says to use Residuals in estimation period to calculate that. However, your work is using Standardized Residuals in estimation period. Probably, I am misinterpreting the paper. Please verify.

Also, would it be possible for you to extend your work to demonstrate t-test for SCARs as well. That is where I think the analysis gets very tricky. And I am struggling a lot.

Thank you very much for your help,

Vineet

Dear Vineet,I am glad that our websites helps you. As our team is actually in the final step of our php/R API development, I was not able to verify all Excel sheets on our website. Please, excuse me for that. You do not misinterprete the paper or the description on our website. The calculation of the cross-correlation is calculated on the abnormal returns on the estimation window. But, as the standard deviation for the estimation window is independent from time and the pearson product-moment correlation coefficient is independent on linear transformations (e.g. set $\hat{X}_i := \frac{X_i}{a}$ and $\hat{Y}_i := \frac{Y_i}{b}$ with $a,b \in \R$ in the Pearson product-moment formula, you will see that you get the same correlation coefficient for $(X_i, Y_i)_i$ and $(\hat{X}_i, \hat{Y}_i)_i$). The reason for the different results resides in the calculation of the correlation coefficient between time series of firm 1 and firm 3 in that Excel sheet (see row 1 and column 3 in the correlation matrix of the Excel sheet). If you look at the formula, you will see that in that cell the window is misaligned (it includes estimation and event window; that's definitly wrong). I will correct this sheet this evening. Please feel free to contact me, if this do not solve the inconsistency. Best,SimonP.S.: Kolari, J. W. and Pynnonen (2010) standardize with the standard deviation with correction for forecast error (as we describe on our website and will do in our API calculation). Actually, in the Excel sheet we do not correct for the forecast error. In that short estimation window of n=10 this leads to significantly different results. Please, consider this. All Excel sheets will be revised and extended (e.g. t-Test for SCARs) after our API is online.