Yes, Kelly Criterion involves the same kind of math. It's all about maximizing geometric mean in an iterated situation where returns are multiplied. (That's why I referred to a product of random variables earlier.) There's lots of applications of this concept.JoMoney wrote: ↑Thu Dec 06, 2018 6:19 pmMany (perhaps most) gamblers would lose to the house even if casinos had zero edge on their games, simply because most have poor bankroll management and take on too much risk pretty much guaranteeing eventual ruin / bankroll depletion when a bad sequence occurs, it is inevitable if too much risk is repeatedly taken.

The Kelly Criterion gives a mathematical formula to determine how much of the bankroll can be bet to maximize growth rate and eliminate the risk of ruin... It will also will tell you the amount to bet on a game with zero expected advantage(EV) is nothing.

Beating the market is a zero-sum game (you can't have a portfolio that achieves above market returns without one that underperforms). If we presume that markets are efficient (even though I don't think they are), then there is no positive expected value from trading, it's just trading different levels of risk/risk preferences. How much risk (relative to the market) the active trader is assuming can be measured through "active share" and seeing how much it deviates from the market return. Most mutual funds don't have very high active share, and the returns typically show a bell curve with the index being somewhere around the middle of the distribution. If you look at the tails (on either side) I'm sure you will find a lot more 'active share'. You would also likely see a lot more left-tail underperforming funds than outperforming funds on the right side of the distribution, and this can be explained by both high fees and by taking too much risk in the zero-sum trading game.

If markets are not efficient, it's still a zero-sum trading game, but it's even worse for traders with no information - if there are traders who do have information and asymmetrical advantages, then the zero information trader has negative expected value.

So in an efficient market (zero EV) Kelly Criterion would suggest you bet nothing on active risk.

In an in-efficient market where you have no special information (negative EV) Kelly Criterion would also suggest you bet nothing on active (actually it would suggest you bet on the guy who has the information, but you presumably don't know who that is).

By the way, in my example, I probably don't really need the "actives" to behave randomly, since there is plenty of randomness in the market itself.