Trading With High Reward-To-Risk

Trading with high reward-to-risk. This is one quote you’re guaranteed to have seen bandied around.

In the trading and forex community it's commonplace to see ‘trade with at least 3R so you can afford to be wrong more often’. (3R being a reward of 3 times the risk taken)

There are problems with this quote and the implications it has:

An assumption that having average wins of 3R is inherently better than average wins of 1R is rife. This is false.

An inverse relationship exists between average payoff (avg win / avg loss) and winrate.

Meaning that, provided you have an edge, shooting for 3Rs will almost always have a lower winrate than shooting for 1Rs.

The common argument for having higher R trades is that it’s ‘psychologically easier’. That getting out of drawdown with these big winners.

Why not try to avoid the drawdown in the first place?

If we equate the expectancy of both strategies to E=0.5R, we find the strategies look like this:

Average payoff = 3R, Winrate = 37.5%

Average payoff = 1R, Winrate = 75%

While both strategies have the same strong expectancy of 0.5, the winrates are very different. In turn this affects the variance.

Variance is the measure of how far a set of data are spread out from their average.

Digging deeper into the maths, the variance looks like this:

3R approach -> Var = 4

1R approach-> Var = 1

With variance, lower is more reliable and means data will be less skewed.

Variance can be eradicated with a high winrate. Consider tracking repellant or magnetic price points to improve on this.

Let's demonstrate with some risk-reward graphics.

This is for 100 trades over 20 different sets of data, risking 1% per trade.

First we have the 3R approach:

For the 3R average wins we can see all 20 accounts are positive (we have a positive expectancy over time).

However, the variance is high, the best curve ends near £2200 and the worst ends barely positive at just below £1200.

Taken from the stats of the chart, we can also note that the worst drawdown was 13 consecutive losers. This is a worry for traders.

Onto the 1R approach graph:

Looking at the 1R average win graph, we see that the equity lines are much closer together and less varied.

The lowest line is closer to the average, and the highest line is also closer to the average. You know what to expect and can plan for it much more accurately.

Our maximum consecutive losses for the 1R approach, over the set of 2000 trades: 5.

Less than half of the other strategy’s drawdown.

Meaning you can position size more effectively, spend less time in drawdown and more time compounding your gains.

In fact the probability of 7 losers in a row (in 100 trades) for both strategies is as follows:

3R Approach (37.5% Wins) -> 97.2%

1R Approach (75% Wins) -> 0.6%

That is astounding.

The stats don't even account for missed trades.

Another qualm I have with the ‘high RR approach’.

What if you’ve had 3 losers in a row (quite common), but then you’re busy or distracted and you miss two 3R winners? You then might have 2 more losers.

By missing just two trades your equity curve has gone from +1R to -5R. That is huge.

Having 2 wins in 7 trades isn’t unreasonable for that edge. Life can get in the way of trading from time to time.

Sloppiness as a side-effect.

I’ve fallen victim to this before and it can be very very dangerous.

‘Oh it doesn’t matter that the entry isn’t perfect, I’m shooting for 3R, I can afford to be wrong more often’

This is dangerous. Taking imperfect setups or setups that don’t fit your edge, because you think you can be bailed out by the high payoff. I’d be very surprised if anyone hasn’t had that thought at least once in their trading career.

Each to their own and everyone has a different style, but these are the statistics behind this particular piece of ‘trading wisdom’. I know I’d prefer more certainty (as rare as that can be in this career).

Trade with high reward, without shooting for pie in the sky targets.