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What would be an ideal way to estimate the covariance of an index with a basket of stocks? For example, should I use one-tail ANOVA test or an individual stock & index F-test?

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Is your comparison vs. the basket of 15 stocks as a whole or vs. each of the 15 individual stocks (the trivial case)? – Ram Ahluwalia Jun 22 '11 at 3:55
Look at the bilinearity property of the covariance function. – Jase Dec 13 '12 at 6:34
up vote 3 down vote accepted

It sounds like you are referring to measuring correlation and/or cointegration. May I suggest you take a look at another question with several answers. I believe it may include an answer to yours as well...

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