At start risk management is far more significantly. But when your abilities improve the importance of risk management will decrease and the importance of profit maximization will increase. The optimal point will change for every trade. It will depend of the way the trade goes. If you take a position and it takes off like a rocket in the good direction, pain will be nihil and the optimal point will be much closer to max reward. If you however take a position and that position stays for hours around break even, pain will be higher and the optimal point will be far away from max reward. The optimal point will be when you say: this is enough (pain and reward). Risk is not equal to pain! Risk is mathematical and pain is psychological. I speak about pain, not gain.
This sounds right for the discretionary trading, but my trading is fully automated. So, I really have no "say" while the system is trading. Thus is the importance of optimizing the risk/reward *before* the system starts.
I see. I wasn't expecting the cliff to be so pronounced. It seems to me you'd want to be close to the red dot, but to the left far enough to compensate if your estimate of kelly/f is wrong and also to compensate if your edge's signal/noise deteriorates enough to shift the dot left on you before you detect it. Maybe another approach would be calculating f based on an empirical sample with various levels of increased synthetic noise added to the returns. I've seen optimal f graphs implied by the returns of, for instance, Dunn capital where they look more like a bell curve. There you might draw a line from the 0 tangent/touching the curve left of the peak. You could make a case that leverage beyond that suffers diminishing returns so it's an appropriate conservative amount of leverage to take. This curve as you have it can't do this or you'd pick '0' as you said. Any of these probably leads to huge relative drawdowns.
Exactly right. The question is, how far to the left of the red dot is enough? That's what I am attempting to quantify. I'll see what I can do by adding some noise, as you suggested. Aside from this, the green dot is so far my best estimate of optimality. The steep cliff is universal (i.e. it can be observed with any strategy). It occurs near the point where the largest loss is magnified by leverage to such a degree that causes the reward/risk ratio to completely collapse. For example, suppose the largest percent loss (of all trades) is 5%. Magnify that loss by 19:1 leverage, which makes it a 95% loss of capital. To recover back to the break-even point, the strategy would have to gain 1900%! So, beyond a certain level of leverage, there is a near certainty of overall net loss, no matter how good the system is (assuming that it had, or will have at least one loss).
Why you think Risk/Reward dependency is hyperbolic? What about if it parabolic? My be it Reward = (Risk)^x, where x > 1 ?
There is always a tipping point - his max return red dot in this case. Think of it this way; say you have an edge at roulette somehow. You bet 5% per spin and win some and lose some but, over time, you are making money. Then, you decide you want to make 20x your return so you bet 100% per spin. Sooner or later you have a loss and are left with 0, which puts you out of the game. 100% is far to the right of optimal leverage for your system. The question then becomes, what % of your account gives the best return. If you go above that level of risk, the long-term returns are actually worse or can even turn a winning system into a losing one. I'm not sure nonlinear's curve looks totally accurate, but I am sure he's right about there being a "Kelly" style max profit peak.
Four years ago I would have totally agreed with you that no hope for bracket traders, but once I dove into it, making rules, keep some rules and throw out what didn't work, kept at it till I had answers to all my questions dealing with commodities. I changed my mindset, I don't trade commodities, I trade risk is what came of it. Took another three years of adding what I discovered and back tested every quarter. But initially getting in, I balance risk to risk, buy/sell futures and right amount of options whether outright owning or debit spreads, I think biggest risk to futures initially is entering, within few days you usually can tell one way or other what is happening or if stopped out-happened. So 3-4 times a day it gets monitored to how much risk I am managing, cause it doesn't really matter what the underlying is. Funny you say you never do it again, I often think of this, all the hours to get to this stage of life. There is no optimal for example as they are way too many "what if's", speed going toward reward, losing percentages, duration left on option, trend, day of the week, day of the month, was it bought discount/prem.
I'm wondering, what would 10 - 20 consecutive losses mean for optimal leverage? Thinking of avoiding catastrophic loss. Is really all else being equal in this graph, ie. no difference in time, number of opportunities per time, fill, margin, agreements, etc.? It still somehow feels like an artificial exercise to me, but haven't had use for leverage so don't know much about it. But it seems if you optimize based on two parameters, that's what you'll get and nothing else. Quite a bit difference in leverage for decellerating gains, but not sure what it means in real trades.
well,in the end, we are all bracket traders, on paper nobody will ever be able to tell after we are gone, it all looks like bracket trades. The difference is what is going on in the mind of a trader. My simple opinion backed up by no fact and can't be defended is, a bracket trader will consistently make bad decisions at bad times. But in the end we are all bracket traders, it's just more about how I think about it.