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rower32
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Joined: July 8th, 2007, 11:59 pm

Regression Confusion

September 21st, 2011, 8:02 pm

Hi I'm regressing daily VIX returns on SPX returns since 2000 the slope coefficient is -3.51. But when I take the natural logs of both index values and run a regression I get -1.25. Why is the difference? I thought when you take a natural log of a series and run a regression the slope is the constant elasticity. But the first regression sounds the same, I mean both regressions sound like how much VIX changes as a 1% when SPX changes 1%, no? what am I missing here? Appreciate the feedback!
 
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daveangel
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Joined: October 20th, 2003, 4:05 pm

Regression Confusion

September 21st, 2011, 8:11 pm

i think you want to regress the change in the VIX versus the change in the S&P or the proportional change. so natural logs should be the right approach.
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rower32
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Joined: July 8th, 2007, 11:59 pm

Regression Confusion

September 21st, 2011, 8:25 pm

Thanks Dave, yeah another friend I just mailed said the same thing. Use natural logs..What confuses me is that if taking natural log is the right approach, what does regressing daily VIX returns on daily SPX returns tell? I am mathematically challenged (obviously) but this is what they teach at school; First find the daily returns, then regress returns on returns. Thanks again.
 
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bearish
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Joined: February 3rd, 2011, 2:19 pm

Regression Confusion

September 21st, 2011, 8:47 pm

Umm - you want to take the difference of the natural logs. That is very close to returns of the form s(t+1)/s(t)-1.
 
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ronm
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Joined: June 8th, 2007, 9:00 am

Regression Confusion

September 22nd, 2011, 7:29 am

I think both approaches should be correct as long as fundamental assumptions of regression are maintained. Ofcourse general style is to have log-diff. You should be okay to see that atleast there is no change in the 'sign' of the estimated coef. However depending on your data there are diff. in magnitude. I feel both should be okay.Regards,