macrocephalopod

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.

Maybe I'm too dumb to understand that Stochastic Efficiency thing. I don't understand why you would start with assuming the optimal leverage of an asset should always be 1. Why would that need to be the case? What is special about leverage 1?

It's obviously not the case and many papers (e.g. Pedersen Betting Against Beta) have shown that empirical best leverage varies across asset classes and alpha within asset classes is -ve correlated with beta, idio vol, and total vol, the opposite to what stochastic eff. predicts.

The "stochastic efficiency" literature (which is like, two guys with zero finance experience) is an example of how you can prove a bunch of stupid results if you make a single stupid assumption.