Hello,
yesterday I thought about the question, why so many people advise to risk no more than 2% of your account. I thought, is that just a rule of thumb or is there maybe a deeper sense behind it.
So I did the following calculation:
Consider a situation in which you expect to be profitable with a probability of 50% and losing also with an probability of 50%. But if you win, you win twice as many pips as you would loose if your trade is not profitable.
So let's make some calculations:
If you first lose 40% and then win 80%, you end up with 0.6*1.8 = 1.08
If you first lose 20% and then win 40%, you end up with 0.8*1.4 = 1.12
What we see here, is that position sizing is not only about risk controling but also about profit maximizing, a higher leverage doesn't need to mean a higher expected value.
I asked myself, where is the optimal position size, to end up with the highest possible return?
Let's do it universallly and call the ratio of the profit trade to the loss trade c (In the example c is 2), then we have to maximize the following equation:
f(x) = (100-x)*(100+cx)
= -cx² + 100(c-1)x + 10,000
To find the maximum we derive after x:
f'(x) = -2cx + 100(c-1)
and set the derivative to 0:
-2cx + 100(c-1) = 0
<=> x = 50 * (c-1)/c
In our example x would be 50*1/2=25, so we would maximize our profit by risking 25% of our capital.
Of course nobody has an "c" of 2, so lets see what c must be to make x = 2:
If we solve the equation for c (with x=2), we get c=1.04.
We can conclude, that we maximize our profit by risking 2% of our account exactly in the case where we expect to earn 26/25 as much as we lose (in our set up scenario where we win in 50% of all trades).
Of course, to get good results you should take your personal (Total Pips Won) to (Total Pips Lost) Ratio for c. But dont forget, do calculate the Total Won/Lost Pips you have to convert them all to one currency and divide them by the leverage you used.
Maybe that helps somebody who also thought about this topic.
Best,
Antoni
yesterday I thought about the question, why so many people advise to risk no more than 2% of your account. I thought, is that just a rule of thumb or is there maybe a deeper sense behind it.
So I did the following calculation:
Consider a situation in which you expect to be profitable with a probability of 50% and losing also with an probability of 50%. But if you win, you win twice as many pips as you would loose if your trade is not profitable.
So let's make some calculations:
If you first lose 40% and then win 80%, you end up with 0.6*1.8 = 1.08
If you first lose 20% and then win 40%, you end up with 0.8*1.4 = 1.12
What we see here, is that position sizing is not only about risk controling but also about profit maximizing, a higher leverage doesn't need to mean a higher expected value.
I asked myself, where is the optimal position size, to end up with the highest possible return?
Let's do it universallly and call the ratio of the profit trade to the loss trade c (In the example c is 2), then we have to maximize the following equation:
f(x) = (100-x)*(100+cx)
= -cx² + 100(c-1)x + 10,000
To find the maximum we derive after x:
f'(x) = -2cx + 100(c-1)
and set the derivative to 0:
-2cx + 100(c-1) = 0
<=> x = 50 * (c-1)/c
In our example x would be 50*1/2=25, so we would maximize our profit by risking 25% of our capital.
Of course nobody has an "c" of 2, so lets see what c must be to make x = 2:
If we solve the equation for c (with x=2), we get c=1.04.
We can conclude, that we maximize our profit by risking 2% of our account exactly in the case where we expect to earn 26/25 as much as we lose (in our set up scenario where we win in 50% of all trades).
Of course, to get good results you should take your personal (Total Pips Won) to (Total Pips Lost) Ratio for c. But dont forget, do calculate the Total Won/Lost Pips you have to convert them all to one currency and divide them by the leverage you used.
Maybe that helps somebody who also thought about this topic.
Best,
Antoni