Alon - Interesting, but this does not answer a question I have about the basic applicability of Kelly to Investing
As I understand it, Kelly criterion, as presented here (and also in the simplified 100% loss assumed) is the % to bet to get maximum growth IN A (long) SERIES OF (Near?) IDENTICAL BETS, where Chance of Winning/Losing is KNOWN and FIXED for all rounds and where rounds are Independent . So if I have coin flips, or roulette - each round is same as all others, Kelly holds.
but in investing - it seems NONE of the above holds.
- The win chance is an estimate with unknown (and probably unknowable)
accuracy
- the Gain/Loss amounts (or %) are also estimates
- in general, each round is different in attributes - if I invest 2 times in
same position, it is likely chance of winning, and the amounts to win/lose
changed the 2nd time around, and if I invest in two different positions even
simultaneously, same thing happens
- There are clear systemic effects making each "bet" not independent. In
Up/Down days/periods, most positions will move in a correlated way
so - is Kelly formula even relevant to begin with?
Have I got anything wrong here?
The usual practice, it seems, is to tell you to look at your AVERAGES and assume they are the fixed values you need.
I.e. assume if you won in the past x% of your trades, your chance of winning THIS time (and indeed, to satisfy Kelly's assumptions - EVERY time) are
X% , and if your average Gain/Loss was G% and L%, assume these for Kelly's formula.
I personally see this practice, of assuming historical average will be what happens in the future as deeply suspect.