Does the correlation between stocks in a sector or between sectors in the S&P 500 have an impact, all else equal, on the S&P's implied volatility / the VIX?
My guess is that the correlation between stocks does not have a direct impact on the implied volatility. See e.g. this answer on how to approximate the implied volatility in a Black-Scholes framework; it does not seem to me that a higher or lower degree of correlation between the stocks would directly affect this approximation. (Of course I understand that a high correlation between stocks might be the result of complacency, which would also lead to a low implied volatility. However, that's not a direct link between the two variables.)
On a higher level, where I am coming from is that I am curious if indiscriminate buying by index funds, which should lower the correlation between the stocks in the S&P 500 or at least between the stocks in a sector, could lead to a VIX of x today not being comparable to a VIX of x 10 years ago.