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If I have 24 temporal covariance matrices (say monthly covariance matrices computed from daily returns of all the SP500 stocks), and I compute 24 betas for variables x and y for every month for past 2 years. Then,

  • What is then the best estimator of beta (e.g. equally or exponentially weighted average of these betas?
  • How can I analyse the stability/variability of the individual beta as well as the estimator of the beta?
  • By looking at these monthly betas can I make any conclusions of the relationship between x & y?

I would very much appreciate, if you have any standard references that clarify my concerns.

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closed as not a real question by Peter Ellis, whuber Sep 24 '12 at 14:11

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ Perhaps this blog post portfolioprobe.com/2011/02/08/… will be of some help. The help might be to suggest that forgetting about beta would be a good move. You don't say what you are really trying to do -- that is important information. $\endgroup$ – Patrick Burns Jan 20 '12 at 15:45
  • $\begingroup$ @PatrickBurns, thanks for the link but as you can see that the value of the beta for variable x (e.g. IBM) and y (e.g. S&P) is not stable (luckily +ve in this example but may even change the signs along with the magnitude) throughout time, I would like to find a stable beta for x and y using the betas I have for each of the 24 months. $\endgroup$ – statnoob Jan 20 '12 at 16:35
  • $\begingroup$ It seems to me that you could process your sample as panel data. $\endgroup$ – Jean-Victor Côté Jan 25 '12 at 18:42
  • $\begingroup$ I may be terribly ignorant, but what is a "beta" in this situation? $\endgroup$ – Peter Ellis Feb 25 '12 at 6:59

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