Conceptual question: Calculating BHAR using eventstudy2

[Sarah Spellauge]

Hi,

I am researching the effect of M&A announcements on stock prices and would like to conduct a long term Buy-and-Hold (BHAR) event study using the user written program eventstudy2. Eventstudy2 supports the BHAR model as specified in the helpfile:

model(abnormal_return_model) specifies the model to calculate abnormal returns. In the current version of eventstudy2, the models RAW (raw returns), COMEAN (constant mean model), MA (market adjusted returns), FM (factor models, e.g. the market model and Fama and French (1992, 1993) factor models), BHAR (buy-and-hold abnormal returns against a market index or factor) and BHAR_raw (raw buy-and-hold returns).

I attached the BHAR formula to this post as maybe not everybody is familiar with the procedure and it may help to understand my problem:

The long term buy and hold abnormal return for a company i is calculated by subtracting the geometric return of a benchmark (R_B) from the geometric return of the company i, whereas the returns are calculated over a specific long term holding period (e.g. 1 year).

The helpfile states that the BHAR are calculated against a market index or factor, i.e. that the benchmark is calculated using a market index or factor. I was wondering how to select which of both models are used to calculate the benchmark? If I use a file that contains the fama french 3 factors, would the command automatically use the fama french 3 factor model to calculate the benchmark returns?

My second question relates to the estimation period in a BHAR event study. In a short term event study, the estimation period is used to estimate the "normal return" (i.e. the return that can be expected without extraordinary events). Does this estimation period plays a role in a long term event study as well? As to my understanding, the estimation period is not necessary in the BHAR approach, as the return of the benchmark is calculated using the event window. Is this correct or did I misunderstand something?

Thank you very much
Kind regards
Sarah

[Thomas Kaspereit]

Dear Sarah,

Thanks a lot for your question.

The easy part first: You are right with respect to the estimation window in BHAR studies. It does not affect the results. In eventstudy2, however, you should be careful with specifying an estimation window together with the minesw option. This might kick out some observations that could be retained in a BHAR study.

Now to your first question: eventstudy2 considers as benchmark return(s) whatever you specify in the options market_returns, factor1... if you run model FM and only market_returns if you run model BHAR. Please also have a look at the idmarket option, which determines which benchmark is applied to which event. idmarket allows you to assign individual benchmark returns to each event.

The FF3 is not suited for BHAR studies, as BHAR models require a single benchmark. Nonetheless, this benchmark (which you have to create) can take into account size, BTM, etc. by means of matching. In the end, however, it will always be a single benchmark per event, in eventstudy2's BHAR model the one that you specify in the market_returns option.

If you want to see an example of a study that uses the 5x5 FF matched BHAR methodology in connection with eventstudy2, I would like to refer you to my current working paper on SSRN: The rise of intangible assets in cross-sectional earnings forecasting and implied cost of capital estimation. Watch out there for the variable PAT_CNT_1%.

Bottom line: You can run all kind of BHAR model (characteristics based, matched-sample) but eventstudy2 will not do the work for you in term of calculating the benchmark returns. They are inputs and have to be provided by you in the market returns file.

Best Thomas

[Sarah Spellauge]

Thank you very much for your reply.

So it would be appropriate to use the market return included in the FF 3 Factors file as a benchmark (my research is US based)?
My code would be:

eventstudy2 securityid date using 01Returns, returns(Return) model(BHAR) marketfile(03FFFactors) marketreturns(mkt) minesw(100) shift(0) evwlb(-30) evwub(365) parallel pclusters(3) proc(1) replace

The SSRN server is currently under maintenance but I will definitely have a look at the paper as I was wondering how to implement the portfolio matching approach.
Kind regards
Sarah

[Thomas Kaspereit]

Yes, Sarah, I think you will be fine with the market returns for now. You can do more sophisticated models later.

Best Thomas

[Sarah Spellauge]

Great, thank you.
Another question that came to my mind when reading through the help file which states that returns are kept discrete if -BHAR model is specified:

if abnormal_return_model is RAW, MA or FM. bnormal_return_model} is BHAR or BHAR_raw, returns are kept as discrete returns, or are transformed to discrete returns if option logreturns is specified.

Would you recommend to keep the returns discrete or activate the -log option so that the returns are transformed to continuously compounded returns when using the BHAR model?

BTW: Shouldn't it say:

...or are transformed to log returns if option logreturns is specified

? As discrete returns are the default setting when BHAR is specified, activating the log option should result in transforming the discrete returns to log ones or did I miss something?

EDIT: I was also wondering whether eventstudy2 will calculate the BHAR over the event window if I do not specify a -car1LB() and car1UB() or whether I have to explicit include -car1LB(-30) and car1UB(365) in my analysis.


Kind regards
Sarah

[Thomas Kaspereit]

Dear Sarah,

Thanks for your additional Q's.

eventstudy2 (es2) internally always runs on cont. comp. returns when using any other method than BHAR or BHAR_raw, e.g. the RAW or FM model.

It internally always runs on discrete returns when using BHAR or BHAR_raw.

The logreturns option just tells es2 if your input returns are cont. comp. or discrete. Thus, whatever model you use, please tell es2 correctly if your inputted returns are cont. comp. or discrete, using the logreturns option if they are cont. comp.

Es2 will then take care of the rest. In your case, which is BHAR, I suggest you use discrete returns as inputs and do NOT specify the logreturns option. You will be perfectly fine then.

[Thomas Kaspereit]

Re: your second question. The default event window of es2 is [-20+20]. The event window determines over which time frame the abnormal return graph is drawn. Further, the car windows have to be within the event window. You get a warning message if they exceed the boundaries of the event window. Feel free to adjust the event window to your needs using the respective options.

Best Thomas