Plot confidence bounds for conditional CAPM conditional beta fit

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sebas
Posts: 2
Joined: Fri Jan 26, 2018 9:32 am

Plot confidence bounds for conditional CAPM conditional beta fit

Postby sebas » Sat Mar 24, 2018 3:20 pm

Hey,

first a big thanks to everyone in this forum! i really appreciate the help provided here. My question is both methodical and statistical.

I have the following issue. I try to break it down for simplicity.

I estimate a conditional capm: Rp = alpha + beta1 Rm + beta2 Rm*DIV(-1) + beta3 Rm*STR(-1) + beta4 Rm*TERM(-1)
Where Rp, Rm are return time series and DIV(-1), STR(-1) and TERM(-1) are lagged information time series

The estimated coefficients allow to calculate a conditional beta for the estimation period:
series cbeta = beta1 + beta2*DIV(-1) + beta3*STR(-1) + beta4*TERM(-1)

Now I want to plot the 95% confidence bounds of the cbeta as well. Is there an easy way to do so? Im wondering if maybe a fit function would help?

My workaround was the following
series cbeta_lower_conf = (beta1-1.96*stdv(beta1)) + (beta2-1.96*stdv(beta2))*DIV(-1) + ....
series cbeta_upper_conf = (beta1+1.96*stdv(beta1)) + (beta2+1.96*stdv(beta2))*DIV(-1) + ....

The results are not that plausible. Could be caused by the model or by my ignorance.

I attached a graphic of a study by Otten/Bams (2004), I want to replicate.

Is my workaround correct? Or is there any other way to get the confidence bounds?

I really appreciate your help.

Thanks in advance!
Sebas
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startz
Non-normality and collinearity are NOT problems!
Posts: 3337
Joined: Wed Sep 17, 2008 2:25 pm

Re: Plot confidence bounds for conditional CAPM conditional beta fit

Postby startz » Sat Mar 24, 2018 3:28 pm

Unfortunately, standard errors don't add.

You need to compute the variance of the sum, taking account of the covariance terms, and then take the square root.

sebas
Posts: 2
Joined: Fri Jan 26, 2018 9:32 am

Re: Plot confidence bounds for conditional CAPM conditional beta fit

Postby sebas » Sun Mar 25, 2018 2:19 am

Thank you so much! That totally makes sense. It felt so wrong to simply add the stdvs =)


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