取引神話と外国為替の数学

=== The parable of danger:reward ratios ===

I suppose all people who begins learning the markets might have heard one platitude:

"Solely open trades with excessive rewards and low dangers!"

What does it imply? It implies that you must solely enter a commerce the place your predefined prize goal is extra distant to your entry than your exit stage. Sounds nice, does not it? I imply, you'll at all times win greater than you lose. Not dangerous?!

Hell no! Let's analyze it.

Though this can be not the complete fact, let's think about that the market is random, すなわち. you haven't any thought on the place/when to enter and which path your commerce ought to have (purchase or promote). したがって, we think about that at every cut-off date there will likely be at all times a 50 % likelihood that the subsequent prize will likely be above or beneath our present prize (or that there's an equal likelihood for the subsequent candlestick to be both inexperienced or crimson). In such a situation prize may be regarded as a random stroll. And as for random walks like this there's at all times and equal likelihood to both attain level A above the present prize or reaching level B beneath the present prize so long as A and B are equi-distant to our present prize.

それにもかかわらず, the chance:reward platitude suggests to make use of a excessive reward to danger ratio (RR), 例えば. 2:1, 3:1, など. We are going to now simply observe what occurs if we use a 2:1 RR. しかし, the identical logic is relevant to different RRs, それも.

Beneath you'll be able to see an image of a possible purchase commerce you can enter:

接続された画像 (クリックして拡大)

The left half, a), exhibits your setup. Assume that you simply'd enter on the open of the candle marked with an arrow. The daring horizontal (黒) traces present your entry prize, the exit prize SL, and the goal prize TP (which is twice as distant from the entry then the exit). Moreover I've drawn a skinny horizontal line (私) which represents an intermediate line which is as distant from the open prize than SL.

Since we now know these ranges that lie inbetween the subsequent greater/decrease stage, we will mannequin our commerce in a discrete method: Each time the prize hits/breaks one line, それは 50 % likelihood of reaching the subsequent greater or subsequent decrease stage. That is proven in b).

After we enter the commerce we've got an equal likelihood of both reaching i or SL. If we've got reached SL our commerce was misplaced, if the prize has reached i it might both go as much as TP (our goal) or retrace again to the entry stage. Every and each state of affairs that may occur so long as our commerce survives may be seen within the resolution tree b). As soon as we all know the prize historical past, we will calculate its chance by multiplying all (0.5) chances alongside the perimeters from our entry (uppermost level within the resolution tree) in direction of the result.

We've got already noticed that (とともに 2:1 reward to danger ratio) we've got an opportunity of 50 % (= 0.5) for shedding the commerce (prize goes straight ahead to the SL stage). それにもかかわらず, our first time we might win (prize reaches TP with out retracing in direction of a decrease stage; the one "TP" within the tree) has a probabilty of 0.5 * 0.5 = 0.25 = 25 %. Though there are additional attainable situations (例えば. reaching SL or TP after retracing a couple of occasions) the ratio of the chances for a win/loss will not change anymore.

What have we discovered to date? (with regard of our 2:1 RR setup?)

1. With a RR of 2:1 you'll be able to win 2 models of cash whilst you solely danger 1 unit of your cash every commerce.
2. With a RR of 2:1 you'll lose twice (2 行事) as a lot as you'll win.

それで, there appears to be an inherent trade-off: In case you change the RR from 1:1 to x:1 (the place x > 1) you'll win extra once you win however you'll lose extra usually. A excessive RR won't ever offer you a bonus (or an edge) in buying and selling!

And from this issues we will additionally see {その} easy grid buying and selling technique the place you purchase/promote/shut your commerce everytime prize crosses a stage won't ever be a profitable system alone.

However the large query is:

How can we overcome the trade-off between the received quantity (pips/cash) and the successful share?

Is it solely attainable with an edge that shifts the successful chance in our favor?

Any solutions/discussions/contributions are very welcome.