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.

Statistics: Posted by Alan — Yesterday, 4:19 pm

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In your opinion then, for the more vanilla derivatives such as swaptions, short rate models are preferable to market models?

Statistics: Posted by frolloos — Yesterday, 4:11 pm

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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...

Statistics: Posted by burnrate00 — Yesterday, 3:01 pm

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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!

Statistics: Posted by burnrate00 — Yesterday, 10:07 am

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At risk of stating the obvious: the LMM model and its generalizations might be a better choice for modelling / pricing rates derivatives.

Not really obvious. It really depends on what you want to price. Furthermore LMM models have a lot of drawbacks: slow calibration and pricing, the correlation structure is difficult to calibrate, the "standard" version (lognormal) doesn't match very well the smile in the current market situation (a term structured HW will provide a much better fit of the smile for the major currencies, even if calibrated only on ATM), lots of factors, etc.

IMHO, better choices are multiple factor extensions to handle the slope correlation (HW2F) or volatility generalization to handle the smile (quasi Gaussian models / quadratic Gaussian models), eventually combined (multi factor quasi / quadratic Gaussian), what remain fast, easy to calibrate and have small dimension.

Statistics: Posted by VivienB — Yesterday, 8:21 am

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What do you think is the best model for trading volatility using only European Vanilla Options and the underlying? And why?

Volatility comes in several flavours. Which one do you want to buy or sell?

Statistics: Posted by frolloos — October 15th, 2017, 6:52 pm

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What do you think is the best model for trading volatility using only European Vanilla Options and the underlying? And why?

Trading does not a formal environment and a good trading idea today might not be a good idea tomorrow. Hence it might be not a perfect idea to talk about 'the best'. For a few approaches it might make sense to keep historical data of your heuristic trades based on different approaches. They also possible might be taking in different moments of time.

Statistics: Posted by list1 — October 14th, 2017, 11:53 pm

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In the binomial model you don't care about mu: if the stock goes up or down ..your P&L of the hedged call is in both cases zero.

This means that the probability of going up -and hence the value of mu- does not matter if you hedge!

outrun, You right. In BS scheme distributions S up-down are given with the help of explicit parameters (mu, sigma). In binomial scheme distributions up-down are given directly and all constructions are given with the help of [$]S_{down} ,p_{down} ; S_{up} , p_{up} [$] . Though I think one can try to present value mu and express hedging ration in terms of mu. Though no one need that.

Statistics: Posted by list1 — October 12th, 2017, 10:38 pm

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This means that the probability of going up -and hence the value of mu- does not matter if you hedge!

Statistics: Posted by outrun — October 12th, 2017, 9:21 pm

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At risk of stating the obvious: the LMM model and its generalizations might be a better choice for modelling / pricing rates derivatives.

Statistics: Posted by frolloos — October 12th, 2017, 5:31 pm

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Your mu is set to r for stock options!

I interpret BS formula in other way.

1) the real stock eq ( mu, sigma ) does not depend on the fact whether options on this stock are traded or not, ie it holds its original sense itself.

2) the option underlying is a heuristic asset, which actually does not exist on the market.

3) this non existed asset makes sense only for non arbitrage pricing strategy, which might be close or might be not close to the price of the option observed on the market.

4) the BS price is a price of a strategy. It does not comprise settlement between buyer and seller.

Statistics: Posted by list1 — October 12th, 2017, 4:46 pm

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