If life could be defined by risk/reward we would all own it Nobody would still be married if they had a stop loss I see no hope for bracket traders
You need a better, more specific definition of "optimality". What you're possibly looking for is an inflection point, I guess. Until you hit that point, for every incremental increase in risk, your increase in reward is bigger than the previous iteration. That is "optimal" could be the point where you maximise your marginal return on risk. But it's you who has to define it...
maybe so, but it would be nice if it was really like that like they tell us in the books I made a good living cutting losses short and letting profits ride,but I would never do it again optimality is just a fancy word for luck I see no hope for bracket traders
Just add all the costs to risk. Make it as real as you can. Be honest and get rid of that theoretical stuff. Is low risk still attractive then? Optimal RR will depend on your inevitable base/average costs. Keep in mind you are optimizing on aggregates, so it wont be real, or are you seriously saying your system is consistently profitable regardless of risk taken? If so, then go for it! However your system does not account for spread, fillrates, possibly more/better opportunities and portfolio management, so a decider for optimization could be made adaptive as well.
a bracket trader puts on a trade and says I have a max loss and when it hits that pain I will take it and lick my wounds, but I also have a target and if it hits that I will walk away happy Then what? A whole life of that? People for centuries have been trying to find some walk around from the old Buy Low Sell High Law
The "optimal" point on that chart would be as far to the left as possible. As your slope turns you are getting less "bang for your buck" than simply leveraging the position. Consider this: .1-1.5 .2-2.2 (your idea of optimal) You can trade your 0.2 and I will trade 2x size at .1. You do not specify a win rate, let's assume it is 50/50. You lose 0.2 and then make 2.2 and are up 2 I lose .1x2 = .2 then make 1.5x2=3 and am up 2.8 Hence, more optimal. Is this chart based on any kind of reality?
This is exactly what I was saying,... but the OP said the curve takes into account the win rate and max drawdown of his system. I find that hard to believe. As we have been trying to explain, the higher the risk the lower the ratio of reward:risk. At the far left extreme is a lower risk with very higher reward which implies a system with lower win rate (think lottery ticket $1 invested for $500 million win at one extreme) and a system farther to the right of that curve would suggest a system with a lower reward:risk ratio and win rate more like 50:50. This appears to be a curve of several different systems not of your system. If the system has a SET amount of expectancy and win rate then varying the risk amount will only change the max drawdown and max profit based on the string and total of winners and losers obtained over so many trades. The random part of the equation is in not knowing HOW those wins and losses come to you in WHAT ORDER. That is why risk management makes such a difference. If over 100 trades you have 50 losses and 50 wins the MAX DRAWDOWN and PROFIT results will be dramatically different if all 50 losses come first followed by all 50 wins rather than alternating win, loss, win, loss, etc. So if you risked too much then those string of 50 losses at the beginning would have put you out of the game. But if they came alternating then you would have been ok. This curve is looking at reward relative to risk and the only way I can see this curve fitting a SET system with known expectancy is if you are trying to optimize a stop loss based on how much to risk vs how much reward you get on your system. Is that what the OP is trying to do? Eganon69
Technically, yes, because on that curve, the reward-to-risk ratio is monotonically decreasing, as you move to the right. Essentially, it prescribes taking zero risk (i.e. no trading at all), which is a conundrum, because clearly, the risk is worth taking, as the reward is far greater than risk. Yes, the chart represents the risk/reward curve with respect to the position size (i.e. leverage) for one of the trading strategies that I have. The Sharpe's ratio of this strategy is about 2.5.
I see, so this is showing diminished aggregate return over a period of time for a large number of trades based on some leverage level proportional to your x? You might then want to read Ralph Vince's books on optimal f. He is the guy that worked with Larry Williams when he was entering the futures world cup. They were looking at an approach to risk similar to Kelly betting. Their intent was to maximize the odds of winning (max return) in a short-term contest with a small account but the information can be useful in general.
Correct. Yes, I am well familiar with both Kelly criterion and Vince's optimal f (which is based on Kelly). On the chart, the red point identifies the "full Kelly" bet. As most traders (and academics) came to realize, full Kelly bet is way too aggressive (in fact, it's borderline irrational, as it's right near the edge of the cliff, from where it's easy to fall down and very difficult to return back). Most rational traders settle for some arbitrary proportion of Kelly (such as 1/2, 1/4, or even 1/10). I believe that there is a sensible proportional-Kelly bet (possibly the green point on the blue risk/reward curve), which depends on the risk/reward curve of a particular strategy, and this is what I am attempting to identify and to quantify. So far, the best recipe that I have is to pick the most extreme North-West segment of the curve. I am working on the more formal, mathematical definition of what constitutes extreme North-West.