I don't have it handy. I did the analysis some years ago. Forgive me, I'm also not inclined to recreate it from scratch. That being said, here are some of the more important points I got from the exercise: (1) it doesn't take infinite amount of periods before the negative expectations show up. The exact opposite is true. In fact, for sufficiently gapping returns (modelled as a simple jump diffusion), kelly strategy returns blow out very fast. (2) I understand your point of wanting to see real data. My point was that even more very clean model data that fits 1 of the 2 iid assumptions, kelly fails outside of a narrow range of values. The chances of any financial return series falling into that tiny class of cases where kelly is optimal is... remote.
It seems like you are not a fan of Kelly. Can you share what other methods you think are better or more practical in terms of "real-world" position sizing and asset allocation? FYI, I am not arguing for or against Kelly. I am just curious to learn what other alternatives are out there.
There's no single answer to this. There's a lot of custom work to figure out what exactly are you trying to achieve, create measures and tools that hopefully measure your goals, and then design optimizations that will get you there. At some point, this process will involve monte carlo path simulations, loss maximization analysis, stress scenario analysis, constrained nonlinear optimizations, etc. Ain't easy. But if it weren't, well trained portfolio quants wouldn't be earning 200+ to start.
%Kelly is a real killer for 99% of the trading systems out there. Although it is anti-martingale position sizing and theoretically it can never reduce equity to zero, it does not accout for the possibility of a large drawdown to begin with and this probability is finite for any finite sample of trades. With a power distribution mass function, the probability of a very large drawdown is finite, although never equal to 1 as in the case of an infinite sample of trades. Having said that, derived actually from basic probability theory, %Kelly is for gamblers only. Not for traders who wish to have prudent risk and money management. I think this article, although basic, offers a good introduction to %Kelly for practical trading. Fixed fractional risk percent method is also anti-martingale position sizing but it offers protection against the finite probability of a large drawdown. The protection depends on the percentage of risk per trade. The lower the better.
Money Management is important as it is helpful in your trading. Please have a look at the following thread, it may help you: http://www.elitetrader.com/vb/showthread.php?s=&threadid=119308
Focus on the concept of deleveraging. For funds that do not care about safety of clients funds, then, yeah, optimal f, etc. B.S. For someone who cares about survival and the ability to be there beyond tomorrow, then think, and then think hard again - survival. It can be intepreted as lower rate of return, cowardly approach. But that is the only approach for all traders who trade for themselves, and getting to old age without being wiped out. p.s. dinosaurs once ruled Earth, but it is cockcoaches survived til now, and probably into the future. =)
So, your entire strategy to the complex problem of trading sizing is... don't bet too much? well.. yes. no kidding. It's about as true as it is tautological. The whole problem is what is "too much" and how to recognize "too much" before it bites you in the ass. You got to put a stake somewhere between zero and too much. Care to share some insight as to how your product will help? (this is a lead in for you to do your pitch).
Keep your position size to a level where if all of the positions lose the maximum likely that month, you don't exceed your (or your clients) max acceptable drawdown. Adjust from monthly timeframe to daily, weekly, quarterly, annually, 5 year time period etc depending on your preference. IMO the main thing to optimize is the long-run chance of survival, all else is secondary.
Agreed. You are obviously entirely right, but you missed the gist of my post. The problem is, how do you determine the loss that is "the maximum likely" in a time horizon. That's the literal million dollar question. If you can do that right, the rest is just arithmetics (or, at least reasonably solvable). The answer is of course there's no single simple answer. That's what I'm getting at.
"The maximum likely" loss in a given time horizon depends a lot on your expected portfolio volatility and expected return, IMO. You may find more on this topic here : http://www.the-actuary.org.uk/697267 and here : http://www-stat.wharton.upenn.edu/~stroud/papers/port.pdf and here : http://www.opalesque.com/ and there : http://allaboutalpha.com/blog/