=== The myth of risk:reward ratios ===

I guess everybody who starts studying the markets may have heard one platitude:

“Only open trades with high rewards and low risks!”

What does it mean? It means that you should only enter a trade where your predefined prize target is more distant to your entry than your exit level. Sounds great, doesn’t it? I mean, you will always win more than you lose. Not bad?!

Hell no! Let’s analyze it.

Although this may be not the full truth, let’s consider that the market is random, i.e. you have no idea on where/when to enter and which direction your trade should have (buy or sell). Thus, we consider that at each point in time there will be always a 50 % chance that the next prize will be above or below our current prize (or that there is an equal chance for the next candlestick to be either green or red). In such a condition prize can be thought of as a random walk. And as for random walks like this there’s always and equal chance to either reach point A above the current prize or reaching point B below the current prize as long as A and B are equi-distant to our current prize.

However, the risk:reward platitude suggests to use a high reward to risk ratio (RR), e.g. 2:1, 3:1, etc. We will now just observe what happens if we use a 2:1 RR. Nevertheless, the same logic is applicable to other RRs, too.

Below you can see a picture of a potential buy trade you could enter:

The left part, a), shows your setup. Assume that you’d enter at the open of the candle marked with an arrow. The bold horizontal (black) lines show your entry prize, the exit prize SL, and the target prize TP (which is twice as distant from the entry then the exit). Additionally I’ve drawn a thin horizontal line (i) which represents an intermediate line which is as distant from the open prize than SL.

Since we now know these levels that lie inbetween the next higher/lower level, we can model our trade in a discrete manner: Every time the prize hits/breaks one line, it has a 50 % chance of reaching the next higher or next lower level. This is shown in b).

When we enter the trade we have an equal chance of either reaching i or SL. If we have reached SL our trade was lost, if the prize has reached i it could either go up to TP (our target) or retrace back to the entry level. Each and every situation that can happen as long as our trade survives can be seen in the decision tree b). Once we know the prize history, we can calculate its probability by multiplying all (0.5) probabilities along the edges from our entry (uppermost point in the decision tree) towards the outcome.

We have already observed that (with a 2:1 reward to risk ratio) we have a chance of 50 % (= 0.5) for losing the trade (prize goes straight forward to the SL level). However, our first time we could win (prize reaches TP without retracing towards a lower level; the only “TP” in the tree) has a probabilty of 0.5 * 0.5 = 0.25 = 25 %. Although there are further possible scenarios (e.g. reaching SL or TP after retracing a few times) the ratio of the probabilities for a win/loss won’t change anymore.

**What have we learned so far?** (in regards of our 2:1 RR setup?)

- With a RR of 2:1 you can win 2 units of money while you only risk 1 unit of your money each trade.
- With a RR of 2:1 you will lose twice (2 times) as much as you will win.

So, there seems to be an inherent trade-off: If you change the RR from 1:1 to x:1 (where x > 1) you will win more when you win but you will lose more often. A high RR will never give you an advantage (or an edge) in trading!

And from this considerations we can also see that a simple grid trading strategy where you buy/sell/close your trade everytime prize crosses a level will never be a successful system alone.

But the big question is:

How can we overcome the trade-off between the won amount (pips/money) and the winning percentage?

Is it only possible with an edge that shifts the winning probability in our favor?

Any answers/discussions/contributions are very welcome.