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burnrate00
Topic Author
Posts: 20
Joined: July 3rd, 2015, 7:08 am

### Beta significance in cross CAR regression

Hello everybody! I am working on the thesis for my Master's degree and in particular I am studying the wealth creation for bidder shareholders in M&A transactions where the target is a digital company. I used a standard event-study approach to calculate the abnormal return for each company and now I am running a cross sectional regression on CARs using some explanatory factors.

The regression line is the following  $CAR_i=β_0+β_1 DTE_i+β_2 Beta_i+β_3 BTM_i+β_4 (Int_i)/TA_i+β_5 RS_i+β_5 D1_i+β_6 D2_i+ϵ_i$

Where $DTE_i$ is the debt to equity ratio, $BTM_i$ is the Book to Market ratio, $Int_i/TA_i$ is the intangible on total assets ratio, $RS_i$ is the ratio between the deal value and the enterprise value of the bidder and $D1_i$ is a dummy that indicates if the acquirer performed more than one acquisition in the studied period and $D2_i$ is a dummy that indicates if the acquirer is a digital company.

The overall results are somehow in line with literature, the $R^2$ is about 11% but the only significant factors are beta, relative size and the first dummy. In particular what concerns me is the sign on the beta coefficient. I expected this coefficient to have a negative sign, meaning: the higher the exposure to market risk as measured by beta, the higher the perceived risk when performing the acquisition and thus I expected a negative impact on CARs... but coefficients are positive with a strong 2.98 t-stat. What I am missing from the interpretation of this factor? Thank you all!

P.S. I did run some diagnostics on the regression.. no heteroskedasticity affects the regression, residuals are well behaved and not relevant multicollinearity appears!

Alan
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### Re: Beta significance in cross CAR regression

I am just guessing. Acquisition targets are typically stocks that have done well and beta is a proxy for that. Perhaps compile some lists of  historical "rumored acquisition candidates" -- see if their beta's are correlated to the emergence of an actual offer. Similarly, the beta could be a proxy for the part of the abnormal return that occurs during the rumor period or, in any event, a part of the abnormal return that you are not picking up because of some arbitrary time window.

burnrate00
Topic Author
Posts: 20
Joined: July 3rd, 2015, 7:08 am

### Re: Beta significance in cross CAR regression

Acquisition targets are typically stocks that have done well and beta is a proxy for that.

Thanks for the input, however I am considering the Beta of the acquirer and not of the targets.
Similarly, the beta could be a proxy for the part of the abnormal return that occurs during the rumor period or, in any event, a part of the abnormal return that you are not picking up because of some arbitrary time window

I am not sure I understand the last part of the sentence. One of the main characteristics of my CARs estimates is that they practically build-up in the first trading day after the event, not much response in the rumor period - which I assume to be prior to the event date -. I don't understand how I could justify a positive contribution from beta to CARs. One idea might be that acquirers with higher positive betas command higher returns, thus higher CARs. But this appears to be a little forced...

Alan
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Joined: December 19th, 2001, 4:01 am
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### Re: Beta significance in cross CAR regression

I see. Well, my point in the last sentence might still apply and since you asked about that, I will elaborate with a variation on the idea.

I will guess the beta is estimated using several years of data. Now the post-event period where the CAR builds up is another period, distinct from the beta-estimate-period -- perhaps overlapping, perhaps not -- doesn't matter. If you picked a random stock during this post-event period, certainly you would expect its post-event period return to be positively associated with its beta. But, since the CAR's presumably are residuals, the issue is more subtle.

So, here is the idea. Suppose you simply made a list of all your post-event periods. For a random stock, you first run the standard market-regression

$R_t = \alpha + \beta R_{mt} + \epsilon_t$.

over the same period you got your beta estimates from. Now, define the "pseudo-CAR" of this random stock to be the sum of its $\epsilon_t$'s during the same post-event periods that you used. The question is: over a cross-section of random stocks, are their pseudo-CAR's positively associated to their beta's? This is possible, due to ARCH effects. If that association is positive for a random stock, it should also hold for the acquirer stocks.

This idea could be wrong, but it's testable.

burnrate00
Topic Author
Posts: 20
Joined: July 3rd, 2015, 7:08 am

### Re: Beta significance in cross CAR regression

Well actually this point is very interesting. Basically we are saying that an autoregressive relationship may exist between the errors from the out of sample estimation and prior returns' errors.
This is how I calculated CARs: starting from $R_{it}=\alpha_i + \beta_i R_{Mt} +\epsilon_{it}$ I obtained $\hat\alpha_i$ and $\hat\beta_i$ from the estimation window, then I calculated $AR_{it}=R_{it}-α ̂_i-\hat\beta_i R_{Mt}$ for the event window (-2/+2 days from the event). CARs are then defined as the sum of ARs over the event window: $CAR_i(t_1,t_2)=\sum_{t=t_1}^{t_2} AR_{it}$ which is basically $CAR_i(t_1,t_2)=\sum_{t=t_1}^{t_2}\hat\epsilon_{it}$. So we are looking for an ARCH effect between $\hat\epsilon_{it}$ and $\epsilon_{it-\gamma}$ with $\gamma \geq 0$. I should be able to test this hypothesis simply by performing an ARCH on returns, right?

Alan
Posts: 9141
Joined: December 19th, 2001, 4:01 am
Location: California
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### Re: Beta significance in cross CAR regression

My suggestion was to compute the $CAR_i$ for a broad cross-section of stocks (not involved in deals), but using the deal event windows. Then do a cross-sectional regression of those against the $\beta_i$ for those same (non-deal) stocks.

If there is a significant positive association (which was what you found with the deal stocks), then perhaps go on to look for an explanation: might be ARCH effects, might be something else.