stock beta v market cap

[brut]

is there a relationship between the beta of a stock v the index its traded in, and its market cap. eg given that the index is market cap weighted, the index's volatility relative to the stock (ie the beta) should be a function of the market cap of the stock?

 

[MrGecko]

Interesting Question. A few pointers:

the index's volatility relative to the stock (ie the beta)

This is the wrong way around. A stock's Beta is the covariance between the return on the stock and the return on the index, compared to the variance of the index.

Also I guess it would depend on the particular index you are looking at, as they are not all calculated in the same way. Even then, while there may be some logic to your argument, I doubt that any tests you did would return statictically significant results. It should be easy enough to run in excel / OxMetrics etc, just alot of grunt.

 

[brut]

thanks for your reply. Thinking about it, a stock could have a negative beta reative to its index, but clearly not a negative market cap. that is to say the market cap is just not big enough to compete against moves in bigger(weighted) stocks. so like you say, it is unlikely to be a statistically significant relationship. I guess that the main point is that once you have the beta, it doesn't really matter.