I was playing around with mathematical formulas in Excel (which I do from time to time ) and came to this conclusion: my account size should be so much bigger than it is and it's all due to some nice math.
I have attached the Excel file that I have been working on.
If I know the number of won and lost trades (WT and LT) over a period of time (at least 100 trades) and average risk:reward ratio (RR) that my system gives me, then I could calculate my account size based on this formula:
AccountSize = InitialAccount * [(1 - Risk/100)^(LT)] * [(1 + RR*Risk/100)^(WT)]
So let's say that my risk is 1%, and over 100 trades I have won 50 and lost 50, and average RR has been 1:2 (this means that RR = 2) then the formula above would give me that with an initial accountsize of $1000, my current account size would be:
AccountSize = $1000 * [(1 - 1/100)^(50)] * [(1 + 2*1/100)^(50)] = $1628 which is an okay profit. I won't get rich but I'm not losing money either.
Now if I think that these sample trades will be what my average trading would look like, how can I make more money? Some of you will jump out and say: risk more you p**sy!
Of course it's the right answer, but how much should I risk and can I maximize my winnings based on my average trading results? Of course the answer is: Yes!
If I take the derivative of the AccountSize function and put it equal to zero, then that will give me what the risk should be to maximize my profits. And it turns out that the result can be put like this:
Risk = (WT*RR - LT) / [RR * (WT + LT)]
So if RR = 2, WT = 50 and LT = 50, then my risk should be 0,25 or 25%. That means that over the past 100 trades my risk should had been 25% on each trade. My AccountSize would have been $361099!!!
Now hold on you might say: risking 25% is way toooo much! And I agree - it is. But if I know that my system is giving me the results mentioned I should definetly not be risking only 1%, that is also wrong. Here is where we have to ask ourselves: how big of a drawdown can I live with without it affecting my trading? Well looking back at the 100 trades, I never had more than 6 straight losses. So If I never want a drawdown that is bigger than a certain % (call it DD) if I have a maximum number of lost trades in a row (LT) then I should not risk more than:
Risk = 100 * [1 - (1 - DD/100)^(1/LT)]
So if most DD I can take is 25% and most number of lost trades in a row that I ever had was 6, I'm gonna exaggerate and use LT = 10, then the most Risk I should put on is:
Risk = 100 * [1 - (1 - 25/100)^(1/10)] = 100 * [1 - 0,75^0,1] = 2,84% or make it a nice round number of 3% (which would give a drawdown of 26%).
Had I risked 3% from the start my AccountSize today, after 50 winning trades and 50 losing trades with a risk:reward ratio of 1:2, would have been:
AccountSize: $1000 * 0.97^50 * 1.06^50 = $4017 which is big difference from the $1628 that I had when risking only 1%.
In conclusion:
Each trader should have a record over his/her trades. That can help us determine how much we should risk depending on our risk appetite, which in turn can help us maximize our earnings. Don't forget the importance of Money managment.
Note that the above numbers are just an example and not what my trading looks like.
A few notes on the Excel file:
You can change the Init.Account, the Risk (in %) and Reward:Risk to your likings, and set NbrOfLosses and NbrOfWins and it will calculate the Maximizing Risk (risk in % that would have maximized the account size based on the above inputs) and Account Size (which is what the account size would have been if the Maximizing Risk was used on every trade).
Furtheron you can check what you should risk at max if you want a certain drawdown after a string of lost trades using Lost Trades in a row, Max DrawDown and Risk (due to DD).
In the middle is a graph of the accountsize depending on the risked % and it's based on the two columns to the right which holds risk in % (to the right) and the account size based on Init.Account, Risk (in %), Reward:Risk, NbrOfLosses and NbrOfWins. Above the graph are the formulas used in the calculations.
I have attached the Excel file that I have been working on.
If I know the number of won and lost trades (WT and LT) over a period of time (at least 100 trades) and average risk:reward ratio (RR) that my system gives me, then I could calculate my account size based on this formula:
AccountSize = InitialAccount * [(1 - Risk/100)^(LT)] * [(1 + RR*Risk/100)^(WT)]
So let's say that my risk is 1%, and over 100 trades I have won 50 and lost 50, and average RR has been 1:2 (this means that RR = 2) then the formula above would give me that with an initial accountsize of $1000, my current account size would be:
AccountSize = $1000 * [(1 - 1/100)^(50)] * [(1 + 2*1/100)^(50)] = $1628 which is an okay profit. I won't get rich but I'm not losing money either.
Now if I think that these sample trades will be what my average trading would look like, how can I make more money? Some of you will jump out and say: risk more you p**sy!
Of course it's the right answer, but how much should I risk and can I maximize my winnings based on my average trading results? Of course the answer is: Yes!
If I take the derivative of the AccountSize function and put it equal to zero, then that will give me what the risk should be to maximize my profits. And it turns out that the result can be put like this:
Risk = (WT*RR - LT) / [RR * (WT + LT)]
So if RR = 2, WT = 50 and LT = 50, then my risk should be 0,25 or 25%. That means that over the past 100 trades my risk should had been 25% on each trade. My AccountSize would have been $361099!!!
Now hold on you might say: risking 25% is way toooo much! And I agree - it is. But if I know that my system is giving me the results mentioned I should definetly not be risking only 1%, that is also wrong. Here is where we have to ask ourselves: how big of a drawdown can I live with without it affecting my trading? Well looking back at the 100 trades, I never had more than 6 straight losses. So If I never want a drawdown that is bigger than a certain % (call it DD) if I have a maximum number of lost trades in a row (LT) then I should not risk more than:
Risk = 100 * [1 - (1 - DD/100)^(1/LT)]
So if most DD I can take is 25% and most number of lost trades in a row that I ever had was 6, I'm gonna exaggerate and use LT = 10, then the most Risk I should put on is:
Risk = 100 * [1 - (1 - 25/100)^(1/10)] = 100 * [1 - 0,75^0,1] = 2,84% or make it a nice round number of 3% (which would give a drawdown of 26%).
Had I risked 3% from the start my AccountSize today, after 50 winning trades and 50 losing trades with a risk:reward ratio of 1:2, would have been:
AccountSize: $1000 * 0.97^50 * 1.06^50 = $4017 which is big difference from the $1628 that I had when risking only 1%.
In conclusion:
Each trader should have a record over his/her trades. That can help us determine how much we should risk depending on our risk appetite, which in turn can help us maximize our earnings. Don't forget the importance of Money managment.
Note that the above numbers are just an example and not what my trading looks like.
A few notes on the Excel file:
You can change the Init.Account, the Risk (in %) and Reward:Risk to your likings, and set NbrOfLosses and NbrOfWins and it will calculate the Maximizing Risk (risk in % that would have maximized the account size based on the above inputs) and Account Size (which is what the account size would have been if the Maximizing Risk was used on every trade).
Furtheron you can check what you should risk at max if you want a certain drawdown after a string of lost trades using Lost Trades in a row, Max DrawDown and Risk (due to DD).
In the middle is a graph of the accountsize depending on the risked % and it's based on the two columns to the right which holds risk in % (to the right) and the account size based on Init.Account, Risk (in %), Reward:Risk, NbrOfLosses and NbrOfWins. Above the graph are the formulas used in the calculations.
Attached File(s)
10till10000.xls
39 KB
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