The Forex Market Random Walk

Building on concepts from a previous article on the risk-reward relation in trading and how it corresponds to winrate, I’d like to explain with some concrete maths behind it – the forex market random walk.

Often when people are talking strategy, they oversimplify the relationship of risk-reward (RR) at outset, and strategy winrate. I’ve previously seen people emphasising the importance of ‘only taking 2R setups’ and ignoring everything else. Reasons cited are bogus experiments such as randomly entering the market and you’ll come out ahead.

That is completely false.

You cannot enter market at random and come out ahead, just because the reward is double what you are risking.

 

What is a forex market random walk?

 

Firstly, let me explain what a simple random walk is, broadly speaking.

‘A random walk is a mathematical object, known as a stochastic or random process, that describes a path that consists of a succession of random steps on some mathematical space such as the integers.’ [1]

Or in our case, random steps on the market.

Assumptions:

  • Markets are completely binary – price can only move upwards or downwards (not sideways).
  • Markets are random – we know that they aren’t in practice due to a multitude of exogenous factors.
  • There are no other trading costs such as spread or commission (I wish).
  • Market takes 10 pip steps.

 

We know that in practice, these assumptions aren’t true, however they need to be made.

Let’s take a walk along a random entry with a 10 pip stop and a 10 pip target:

We have two directions, up or down. Due to randomness, each of these directions have equal probability (50% each). Once we reach stop or target, the walk is over.

 

 

This is the most basic form. We see that we can step in either direction, but not stay still. Once either step is hit, the game ends.

 

2R is better though, right?

 

Let’s take a look at a 2R random walk. The same assumptions as before, except now the game doesn’t end until 20 pips is reached, or -10 pips.

This time, we will break it down to 4 separate trades, so that we can follow their journeys:

 

So are you saying that a 2R trade only has a 25% chance of reaching target?

 

No.

Don’t forget about the trade which is back at 0. In simplified terms, we can think of this trade as having ‘reset’. This leaves us with 3 trades having completed.

1 is at target, 2 are at stop – this gives us a 33% winrate, on a 2R target with a random entry.

 

What about managing the trade better – breakeven when at +10 pips?

 

Absolutely do not do this.

Of course you want to ‘cut your losers‘ and ‘protect your profits’ but this is the complete wrong way to go about it. Let us rewind to the two trades which are still open and at +10 pips

At the +10 node, there is a 66% chance of hitting target and a 33% chance of hitting stop (effectively shooting for a 0.5R, the inverse of what we found – 33% chance of winning with a 2R target).

 

By moving to breakeven in this example, you’ve shifted the odds of winning against you, just to ‘protect’ what you have. But you haven’t protected anything. You’ve sacrificed an open profit of +10.

The trade at outset had a 33% of target. Moving to breakeven gives the trade a 25% chance of reaching target (50% * 50%).

This is a flimsy argument in this case, due to the expectancy of any node being 0 (there is no edge in randomness). However, the way most people trade, their expectancy is highest at their initial entry (perhaps a turning point) and weakens the further it gets from that point. This means that you’ve weakened your chances of seeing target, in addition to the edge being weaker already.

Trading with a magnetic target can help to alleviate this somewhat, as the trade target provides as much basis for the trade as the entry point.

 

Wrapping up

 

If anyone tells you that a 2R target is better than a 1R target ‘because your reward is more!’, point them towards this article. In a strategy vacuum, all targets should have similar expectancy, but as the targets move around, the winrate does too – don’t forget about the forex market random walk.


Also published on Medium.

5 Replies to “The Forex Market Random Walk”

    1. No no, trade with whichever R fits your strategy, your style, your psychology. This is to simply demonstrate that just by placing 2R instead of 1R targets, you haven’t improved your bottom line – in actual fact it’s stayed the same. Hope that helps! Thanks so much for reading and commenting!

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