Ergodicity, diversification, and redistribution

My book on Ergodicity: gumroad.com/l/...

[@MuchoMate]

Am I correct to assume that the virtuous redistribution effect of the portfolio is what happens when one owns an index (sp500, etc)? Or not really?

[@DellAnnaLuca]

I'm not sure how much the effect applies to an index that's weighted based on market cap; in that case, you get diversification, not redistribution.

[@AndreaCasalotti]

Your basketball example works only with specific sequences. If you average over all possible sequences, there is no gain. So what is the advantage of the ridistribution strategy?

[@DellAnnaLuca]

There is gain across most sequences. I created this 2-minutes video to show what happens if we look at distributions of outcomes: www.loom.com/share/1d04c97d481849608a0f14078ed3d26e

[@glorydays1565]

This question needs to be adressed on a much more fundamental level. You're absolutely right that (on first glance and retrospectively) there would be no overall gain from the perspective of the ensemble (all sequences taken into account) if every _individual_ sequence had earned the ensemble average (no volatility at all). But if any individual sequence is closer to the ensemble average, it makes the future of the system as a whole and its individuals more robust. Specifically, its future ensemble average won't be contingent on the future decisions of a single entity (sequence). After all, the _future_ ensemble average is a (uncertain) function of time from today's perspective. Also think about benefitial secondary effects of a more robust system that may increase the ensemble average itself.