How to position size to maximize return over capital?

I can't find any thread talking about position sizing, so I decided to start one to discuss.

After finding a profitable system, next step is to find the right position sizing system to maximize profit % over capital and do compounding.

Assuming my capital is $10000, I'm currently risking maximum $200/trade. Using the typical industry 2% risk per trade.

On average, my system gives me 8 trades per month.

My longest losing streak was $273, in 28 days, 6 trades. I'm using a dynamic system, I often move my stops, that's why when I lose, I rarely lose $200/trade eventhough I risk $200 initially.

2nd longest losing streak was $196, in 16 days, 5 trades.

With $10000 capital, what is the maximum risk per trade I should use to maximize my profits at the same time not risking too much to eventually blow up the account?

Here is how I think I should do it.
I assume 2 longest losing streak coming together. $273 + $196 = $469.
Even though it's not likely but it's still possible, so in order to make sure my account is almost impossible to blow up, I have decided to multiply $469 x 3 = $1407 as my capital, for risking $200/trade.
Now, if I have US$10,000 as capital, then I should risk $10000 x $200 / $1407 = $1421 per trade to maximize my profit % over capital. That's 14.2% max risk per trade.
And I will compound it using this 14.2% risk per trade when the account grows, until I experience a bigger losing streak, only then I will change my risk% again.
Please give me your feedback guys and girls.
Additional stats about my system.
Average loss per trade = -2.9%,
Average win per trade = 3.6%,
Winning ratio = 62%.

If you get a losing streak you have to recover this DD. During this recovery period you don't want to take additional losses that increase the DD. So it's a good idea to size the trades such that a winner always covers a loser. You have more winners than losers so the account should grow. Technically this doesn't maximize the profit but gives a good probability you'll recover from a DD.

Let be x your trade size. x is between 0 (skip the trade) and 1 (100% of the account).
If you lose, your account is multiplied by 1-x. For example with 1% (x=0.01) your account would be multiplied by 0.99 ($10000 -> $9900).
You have a RR of ~1.24 (3.6/2.9) in average. A winner multiplies the account by 1+(36/29)x. For example with 1% your account would be multiplied by 1.0124 ($10000 -> $10124).

A loser followed by a winner would multiply the account by (1-x)(1+1.24x). You shall size such that this is always in your favor. I mean the net result should increase the account. You search x such that (1-x)(1+(36/29)x)>1 and is maximized. The solution is x = 7/72 ~ 0.09722. So 9.7% is optimal in this respect if your stats are correct. But keep in mind that after 7 losers the account would be divided by 2! That's certainly too much.

Are those stats based on forward testing on a live account or backtesting?

Thanks PipMeUp for your view. Nice formula you have there. I presume your calculation is cater for a 50% winning ratio system? So far my win rate is around 62%. And the problem with my results is the winners and losers have a very wide range. My winners range from 0.07% to 26%, while my losers -0.28% to -23.7%. So using it's average may not be a good idea.

So my focus is on the drawdowns. I need to make sure I position size small enough to stay alive when the drawdown comes, and bet big enough to have the steepest gradient on my equity curve.

SM02, those stats are from my live trading account.

your loser -23.7% is sort of irregular since i feel your method seemingly mature and stable (based on your description)

why do you let a loser run that long and it is not a common action in your trading? what i'm saying is that if you usually don't let a loser run that long, why don't you just cut it? and if you should've cut it, you should not consider it when planning for postion sizing......

my statistics are similar to you, and my impression is that for 10000$, 500$ loss per trade, can bring in satisfactory growth (to me, of coz; might not be for you), DD might well be over 3000$. i never put in serious numbering work like pipmeup.

but still, you look at your live records, just use a lotsize factor to simulate/restore your trading history with different lotsize, you can at least feel the pain/ecstasy along the varied equity change. that's real feel.

If you're system gets more than 3 consecutive loses then I advise you to never go over 1.5 percent per trade. And with 60 percent then with your system 4 consecutive loses are possible. Just my two cents.

Thanks Charvo & saneblane for your comments, you guys did give me some good inputs.

Here is my past 6 months Equity curve, total 50 trades, with a fix position size of max 2% risk per trade. My results is around 8% profit.

If I use the same fix position size X for the next 6 months, and I assume the 2 DD came early and together, I will still be profitable all the time.

And there seems to have some room to risk more if I'm willing to risk all my profits.

If I'm willing to risk all my profits, I can increase my position size by 60%, 1.6X. Then I may be able to increase my profits to 20% per year.

Now, if I'm willing to go crazy and risk all my 10k capital. Increase my position size by 22X, maybe I can achieve a return of 185% per year? Let me know if my estimation and assumptions make sense?

you actually tried only a few scenarios out of hundreds of possible outcome

say, it is actually not hard to try this:

you know your win/loss ratio, you know your RR. just run a monte carlo test in excel.

or draw a simple test chart and keep running it tens of times, you'll see the potential (return) and risk with higher bets. hope you understand my excel file, it is self-explanatory. type any number in those blank cells, the chart and numbers will update randomly -- like a dumb simulation.

it is really a double side sword, i don't know how to raise profit potential without risk being raised too. however, i do feel that if with ReturnRisk > 2 and win% > 50%, position sizing with 5~10% per loss might be highly wonderful. 2% per stoploss is too conservative for me (again, for me only, lol)

You see the thing about trading is your state of mind plays a big role also in the outcome of your trades and that is something that can never be back tested. Look at your chart at 41 for example at DD1 AND DD2, if you hit that losing spell in real life you are going to feel like shit, and you might even start second guessing yourself and closing trade that could have gone your way short and decrease the win/loss ratio. You might be losing sleep checking you trades every 5 minutes and trading can take over your life when the stress of open positions becomes all you think about. I am not denying your chart, but unless you have nerves of steel it's not going to be easy.

The 1 percent rule was made so you can be objective with every trade. Another thing that is also important that you cannot get on the chart is experience the fact that you servived a year in trading can do wonders for you ability to execute your trades without bias and give you more confidence to walk away from a losing trade without thinking about it and think about it as just the cost of doing business. You can try to aim for something like 4.5 percent a month and with compounding you can reach close to 100 percent and that would be the safest way I think to do it. Slow and steady win the race. Below is a chart of 12 months traded at 4.5 percent compounded each month. If you can get 5 percent a month then it's even easier but that might be too much for now, hope it helps.

1$ 450.00$ 450.00$ 10,450.00
2$ 470.25$ 920.25$ 10,920.25
3$ 491.41$ 1,411.66$ 11,411.66
4$ 513.52$ 1,925.19$ 11,925.19
5$ 536.63$ 2,461.82$ 12,461.82
6$ 560.78$ 3,022.60$ 13,022.60
7$ 586.02$ 3,608.62$ 13,608.62
8$ 612.39$ 4,221.01$ 14,221.01
9$ 639.95$ 4,860.95$ 14,860.95
10$ 668.74$ 5,529.69$ 15,529.69
11$ 698.84$ 6,228.53$ 16,228.53
12$ 730.28$ 6,958.81$ 16,958.81

Charvo, thanks for the file, I only need to know the possible worst scenario. It's difficult to accurately mathematically model my system. Maybe need to fit in a normal distribution formula in there. Anyway, I only need to know the worst scenario to position size, to make sure I can survive the possible drawdown. The profits will take care of itself.

Saneblane, yeah I agree with you on the psychology effect. That's why I need to understand my system well, to expect the drawdown will come one day, and not surprised by it. In fact maybe I should even increase my lot size after the drawdown if I'm confident with my system. And it's important to only trade with the money you are willing to lose all, not pouring your whole networth into this game.