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Saturday, August 6, 2011

The Dynamic position size paradox

In my previous post Risk a percent of your account per trade I talked about money management and capital protection basics, by only risking a fixed percent of your trading capital per single trade, and showed how to adjust your position size in a Forex play to meet this goal regardless of how far or close your stop loss is from the entry.

Given that we adjust the risk at our will by regulating the position size on every trade, we can say we are using a dynamic position size technique. Now let's analyze this interesting occurrence that has more to do with Math than trading but it is something to keep in mind for our game.


Suppose you have $10 000 in your trading account and you have a system with a 1:1 risk/reward ratio. This ratio means that the distance from your entry point to your target is the same as the distance from your entry to your stop loss. Your winner trades will be the same size as your loser trades. Obviously, with such a system you would need to win more than 50% of the trades in order to be profitable. But you expect that as long as you win half your plays, you are at breakeven.

Let's also say you risk 2% of your account per trade, and you target a 2% growth per trade.
If you win 5 trades, winning 2% on each, and you lose 5 trades, losing 2% on each one you would expect to be at break even right? It is a common illusion, however it is a fake one!!

Assume, you win the 5 trades first in a row, and then you lose the other five. The progression is as follows:

Starting capital 10 000
First winner trade +$200 = $10 200
Second winner trade +$204 = $10 404
Third winner trade +$208.08 = $10 612.08
Fourth winner trade +$212.24 = $10 824.32
Fifth winner trade +$216.49 = $11 040.81

First loser trade -$220.82 = $10 819.99
Second loser trade -$216.40 = $10 603.59
Third loser trade -$212.07 = $10 391.52
Fourth loser trade -$207.83 = $10 183.69
Fifth loser trade -$203.67 = $9980.02

What the fuck! 5 winners, 5 losers, winners of +2% and losers of -2% and I am down! The beauty of this is that the order doesn't matter at all, put the 5 winners after the five losers, or combine them however you want, you will end up losing money. To prove my point let's make it simpler, and consider the same $10 000 account, but only two trades, one loser and one winner:

First winner trade +$200 = $10 200
First loser trade -$204 = $9 996
You end up losing

Reverting the order:
First loser trade -$200 = $9 800
First winner trade +$196 = $9 996
You end up losing again, the order doesn't matter.

How to solve this problem?
One way is to target a little more than what your are willing to risk, so if your risk/reward ratio was 1:1, you probably want to target 1.05 : 1, thus putting your targets farther. The problem with this approach is that probably your system worked because putting the targets and the stop losses at the same distance to the entry was part of its nature and success! Maybe changing the target arbitrarily causes unexpected consequences like suddenly getting less winning trades! Maybe on the other hand it doesn't really affect the number of winners, and in that case you are good to go.

The other approach is to risk a fixed percent of your account but instead of calculating the risk based on the current account balance, you base the calculation on a fixed initial account balance over a period of time. In our case with the $10 000 account, for example, I would be risking 2% of my initial $10 000, targeting $200 winners or $200 losers for a whole month, regardless of whether my account is growing/changing in total balance. And by doing this, the numbers won't betray you, if you win 5, and lose 5 times risking 2%, you will be at break even this time. The next month, I consider my new balance, let's say I grew to $11 000, then for the whole month I will be risking and targeting 2% of 11 000, until the month is done.

Those are just a couple ideas to consider so that the numbers don't play games with you when using dynamic position sizes to adjust your risk per trade. Remember, this is not a zero sum game, it is a negative sum game!! In order for you to win, somebody has to lose, add broker commissions and/or spreads to the mixture and there you go! So, knowing all the ins and outs, saving a penny here and there might make a difference in the long run.


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