People are waaaaay overcomplicating the whole issue. Say you want to throw a ball as far as possible. You analyze the problem and the physics tells you to throw the ball as hard as possible at 45 degrees. The "kelly critrerion" in this case is "45 degrees". That is all it says. Should it be used all the time? No, since "the law of gravity of markets [equations of motion]" are statistical and not deterministic. So if the law of gravity changed randomly, then the optimal angle might be something else. What fraction of Full Kelly should you use? Optimal-F seems reasonable. That's all folks.
The Kelly number has NO inputs from historical number of trades. It is determined purely by future win rate and payout odds. Now, you may choose to estimate the future win rate and payout odds by looking at past historical numbers, but that is nothing to do with the kelly formula, it is your own approach to the tricky problem of how to calculate the inputs into the Kelly formula. In the Fukushima example, the correctly calculated trade odds would already incorporate the worst case loss from that or any other market shock. If a user of the Kelly formula underestimated the risk of loss, and thus had totally incorrect trade odds, then it is the fault of his grossly erroneous odds estimates, NOT the Kelly formula.
Doesn't optimal f rely on worst historic drawdown? That makes it totally useless for calculating size based on *future* worst drawdown. Someone who had a strategy that rarely loses much money, and then once every 5 years loses a huge amount, would be totally overtrading if they were within the first 5 years of trading their strategy's cycle. It would also mean that two traders with identical risk tolerance would take an identical trade on radically different size, purely based on their differing max drawdowns from the past, which is logically inconsistent (since the only inputs into correct size are trade odds, total risk capital, and risk tolerance). The only conclusion is that optimal f is logically inconsistent. Your physics analogy is misleading because the 'odds' (gravity, the mass of the ball etc) are known with precision, and it's the execution (throwing at 45 degrees) that is difficult; whereas with trade sizing, the odds are hard to estimate, whereas the execution is trivial (even a novice can choose their bet size with 100% accuracy).
I agree that risking forward by looking backwards is fraught with danger. I suppose you could trade a fraction so small that it would no longer be worth trading. Alternatively, you could start with $10M, risk enough to make $100,000 a year, and be certain never to blow out. That would work for me fine. The problem is the $10M to begin with. So most people [with an indisputable edge] push the limit a bit and risk getting pulvirized by planes flying into a building etc. In the meantime, if you have something that works with extreme regularity, you are minting coin. If it is based on account size and things are calculated using [log] percent, why not? Read what I wrote once more. You will see that your objection is already dealt with. The analogy as stated with the caveat is perfect.
From what I understand, figuring out optimal-f is a complicated process. Perhaps I've heard wrong. How do you calculate optimal-f? Thanks.
See? This always happens. Somebody here starts singing the praises of optimal-f, then somebody else asks why is optimal-f superior to Kelly or how do you calculate optimal-f ... and the answer is always the same: TOTAL SILENCE I think all of us who aren't for whatever reason personally invested in pushing this stuff can agree that optimal-f really stands for optimal-fraud.
I've always thought that it's called optimal-f because if you use it then you'll be optimally-f***ed...
Ralph Vince used to post here. It seems his answer for when anyone would ask him to explain optimal-f was always "Buy my $40 book." Nuff said.