Hi Guys,
First of all - this is my first post so I'd like to take this opportunity to thank you for everything I've learned from you so far.
I've got a question in the scope of statistical analysis of stocks and indices.
How would you interpret having low R-squared values for most of the companies in a given sector combined with having betas below 1? I know this is mostly theoretical, I'm just looking for any possible explanations.
Thanks, Paul
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Low R-squared means that the model is not good at explaining the stock's returns. More generally, it likely means that the stocks you are looking at are highly impacted by unsystematic risk.
Assuming you are using a standard OLS regression, R-squared is the explained sum of square differences over total sum of square differences:
R^2=ESS/TSS
Like unfriend said, this means that your explanatory variables are not controlling for much of the variance in the stock. I don't think this really has any bearing whatsoever on what the coefficient on beta is; you should be looking at the standard error on beta and considering the corresponding p-value. If this shows your coefficient to be significant then a low beta obviously means that the stock has a lower systematic risk. Importantly, this says nothing about idiosyncratic risk - this could also be low.
Both above posters are correct
All right, I think I've got this - I run some p-value calculations and betas turned out to be statistically significant throughout the whole sample.
Thanks for your quick responses guys!
R squared is correlation, low R squared means its not correlated. Number is typically in a decimal that you can convert into a percentage. There are excel functions ( I think CORREL) for these.
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