[pedrocr]

>This is true in aggregate, with the additional caveat of over an asymptotically long timeline.

This is true over any timespan. At any point in time the active part of the market holds the same stocks as the passive part of the market and thus has the exact same risk and returns. This is as true over a century as it is over a month.

>not only can active funds invest in assets outside of the index (other stocks, real estate, futures, options, etc.), but active funds can also have more profitable allocations

If your active fund is investing in different markets then it's not comparable to the index. If there's an advantage in investing in those assets the solution isn't to buy the active fund. The solution is to find the index funds that will also give you exposure to the same assets and buy those instead gaining the same advantage of the same returns with less fees.