## 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

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?

Sebas
Attachments Unbenannt.JPG (16.82 KiB) Viewed 767 times

startz
Non-normality and collinearity are NOT problems!
Posts: 3507
Joined: Wed Sep 17, 2008 2:25 pm

### Re: Plot confidence bounds for conditional CAPM conditional beta fit

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

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