Is it reasonable to "beta-weight" Individual IV to Index IV?

For example, if SPY IV crushes 179 basis points, or ~10% of its total IV of 17.9% (Source:Barchart), is there a way to tell with any predictive power what that will do to the IV of the SP500 Underlyings (AAPL in this case)?

 

Not with any chance of accuracy. The SPY is simply the Beta - as opposed to the individual component or Beta, Alpha, and an individual stock component related to the properties of the individual stock. Plus some of the component stocks may move contrary to the overall index.
However, if they get too far out of line desk may enter into a dispersion trade with the expectation of some reversion - they may trade a smaller basket of the components against the index.
Look at the vols of the Fang components and compare them to the FANG options themselves - a bit easier because it narrow-based.

 

Surely there is.. check the scholarly literature or work out the formulas

 

Not sure i follow , there should be some nonzero (random) amount if predictability

 

not regular beta but “vol beta” which like regular beta is a regression of both realized vol time series.

as ajacobson said, it’s crazy noisy. Not that different from regular beta