Nobody is disputing the definition of beta, I just merely mentioned that beta and correlation are two separate concepts. In any case, the definition of beta is (mainly) for portfolio to broad market, even estimating beta for a single stock to broad market is a fishy proposition.Quote from Kevin Schmit:
Not entirely separate, as correlation is a component of Beta. Beta is covar(a,b)/var(b). Covar(a,b) is cor(a,b)*sigma(a)*sigma(b). So Beta can be written as cor(a,b) *(sigma(a)/sigma(b). IOW, Beta is correlation scaled by the ratio of vols.
Many stock pairs have stable, invertible short-term hedge ratios measured in a number of different ways. People actively and successfully trade stock pairs in delta-1 space on much shorter time horizons, so no reason to expect that it would "fail" in the options space.Quote from Kevin Schmit:
He was, in his post, as far as I can tell, referring to the correlation component of Beta.