macrocephalopod

Yeah. In "old man quant world", we'd say that you can diversify the (unrewarded) idiosyncratic vol away by diversifying (or indexing), to harness the equity risk premium.

A common misconception is "the ERP doesn't exist if you look at an individual stocks". The truth is that the variance term for an individual stock contains a component that can be trivially removed by diversifying.

It exists, it's just explainable.

Yeah exactly. The stock contains a component of idiosyncratic volatility, which the index does not.

In your language "the geometric return of the index is higher than the individual stocks, because the index has reduced variance"

Right, but why say the idiosyncratic vol is unrewarded, when the premium is explained by that idiosyncratic vol? How is it not rewarded correctly then?

As you noted earlier, the expected geometric return of a single stock is a lot closer to the risk-free rate, than the geometric return of the index. This is because the stock contains "stock-specific variance" that washes out (nets off on average) through diversification.