It seams running full kelly on a part of the capital and keeping the rest in cash balance will produce the same percentage return after 12 months duration as running half kelly on the whole capital available. Even if max draw down are higher on part/fraction of the capital. The worst case draw down will be lower on the whole. Thus lower over all risk. a) Half kelly on $10000 -> 200% return over 12 months b) Full kelly on $4000 ($6000 in cash) -> 200% return over 12 months Same annualized return but a lot lower MDD on the second one. What is your thoughts on this? seams smarter to employ full kelly on a fraction of account to me (if I'm not wrong about it).
The full kelly risk strategy will start to diverge and outperform more and more for each passing year.
What do you mean by “smarter”? Running full kelly on half account, is essentially like having a global portfolio of 50% cash and 50% risk on. As you increase the rebalancing frequency, the strategy will mirror half Kelly more and more. From a standpoint of optimizing mean terminal wealth across your entire forward distribution, full kelly is “smarter”. Any time you take a step down from that, you’re sacrificing theoretical expected value for a reduction in variance. And I think regarding portfolio volatility, it’s easy to conceptualize the % volatility figure, but harder to project out the implications of high var on the 2 std dev floor of your fwd distro across extended time, for example. You may have a decent strategy that solves for 60% pft vol per a given time step and you feel okay about that. But that means on the unlucky paths you can easily lose half your capital in that time step. And the same thing could happen again several times in a row! At least for me, there’s a flex point where it gets pretty hard to stay engaged and not get defensive, which if you de-risk you’ll essentially be locking in a lower mean terminal wealth figure, on a now much smaller capital base, so in practice you end up trying for full kelly but realizing the worst of both worlds. On the bright side though if you keep getting bad var, eventually it doesn’t matter anymore and you might become content again and willing to go down with the ship without much angst Let alone all the problems with being penalized with -$ ev at fully kelly for any mis-estimations of fwd vol, gaps/jumps, etc. Whereas at half kelly vol coming in a little higher actually adds some theo ev. In practice almost everyone who makes good money eventually ends up segmenting their capital, or lowering their (targeted) vol figure over time. Our lives aren’t really long enough to get enough instances to raise nearly the entire full kelly distro over the lower vol distros, outside some niche higher frequency stuff. Pair all that with the decreasing marginal utility of wealth and full kelly isn’t very practical. I would advise actually taking x% of the money you aren’t risking out of the account and rebalancing when necessary. If you’re targeting half kelly and you miss some tail risk, you could way overshoot your vol target at the worst possible time. Sometimes in tail events, external limiters like broker partial liquidation, leverage constraints, siloed capital, etc. can end up helping us survive when usually they are an annoyance. One way or another the real world ends up being a lot less tidy than our theoretical plans
Yeah, you can use Full Kelly on how much of your capital you are prepared to lose. So if you got 100K but only prepared to lose 20K. Then intially calculate your risk based on full kelly with 20K. For stocks, margin requirements will eventually get in the way. Even for overnight futures margin will eventually get in the way of going full kelly if you need to hold multiple positions. Only intraday trading where you can get 50x or 100x and higher leverage, allows easy full kelly without worrying about margin.
At some point, when your risk capital has grown much larger than your safe capital, you will want to stop using Full Kelly, as full kelly drawdowns are hard to stomach. Its easy to think you can stomach large drawdowns, eg 90% drawdowns on a 1million account, that you grew from 100K to start with. In reality you can only do that kind of drawdown if your net worth is already multi millions. Or maybe you can do those kinds of drawdowns a few times early in your trading career, but after a while you wont be so willing to give back large profits. Your drawdown shock absorbers will eventually wear out. I have found its not just the size of drawdowns, that is only half of it. The other half is duration of drawdown. If your trading gives a multi year drawdown, that is hard to live through if your draw down is 50%. But obviously not so bad to live through if the drawdown is only 15%.
Take a look at this Ed Thorp paper: https://www.edwardothorp.com/wp-content/uploads/2016/11/TheKellyCriterionAndTheStockMarket.pdf I don't think your half Kelly and Full Kelly cases are equivalent. But I am math challenged, can't do the math to determine yes or no. By the way, those who practice Kelly like Dr Thorp, use fractional Kelly, around 1/4 or 1/3 to avoid and reduce the risk of ruin without too much dilutions on the returns.
It's trivial maths that (x*0.5)*c = x*(0.5*c) And if you stopped trading after losing half your money they would be identical. Which you use is basically framing GAT
Trivial? The payoff curve f(c) is a nonlinear function, so is x*f(0.5c) = 0.5x*f(c) in all cases? Are you supposed to stop after losing half your money in all cases or trade for the same fixed time period?? Anyway I am not a mathematician or a statistician, just asking you math guys a couple of questions.
I do get that risk/reward is the same at equal draw down. But one got to give the strategy leeway to perform within the bounds defined by observed strategy metrics to let it do its thing and perform optimally. An other issue is possible strategy degradation over time. If one got a hard floor on draw down (fixed allocation + full kelly) the maximum loss will be less if things go haywire.