Understanding the Reward/Risk and Win/Loss Ratios of a Trading System

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Is it possible to characterize the general likelihood of the success or failure of a trading methodology by examining merely two of its characteristics?

May sound a little hard to believe.

Interestingly, the relationship between these two attributes is not only a fundamental underpinning of good analysis but it also provides sufficient information to answer the pivotal question of any strategist: What combination of rewark/risk and win/loss yield profitability over the long run?

A quick review of terms for those that may be unfamiliar with them:

Reward/Risk: The ratio of the distance from entry to exit versus the distance from entry to stop.
Win/Loss: The empirical (observed) probability of wins versus losses.

Picking a naive starting point, for example 1:1 RR and 50/50 W/L, produces something of the following nature:

Click the graphic to see it in full resolution and observe the attributes of this “starting-point”…

Having done so, the next intuitive question might be: How much does the RR or W/L need to shift in order to push things into profitable territory?

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Shifting the W/L to 70/30 and leaving everything else constant provides an arbitrary estimate in the direction of profitability:

This is in fact quite an overshoot, but the modeled results indicate that a combination of 1:1 RR and 70/30 W/L is profitable over the long run.

A more elegant and precise answer to the question can be obtained by iterating the process demonstrated by the naive guessing method across all possible RR + W/L combinations (within reason).

Doing so in this example means the 1,000,000 data points (1,000 paths x 1,000 trades) in each individual graphic above are resampled across a grid of the RR + W/L “pairs” at a provided interval. The resultant outcome yields an intuitive graphical answer to the original question:

The plot on the left illustrates the conical output, along with the intersection plane (in this case break-even).

The plot on the right is a top-down view.

Tracing the conjectural example of 1:1 RR + 70/30 W/L onto the right plot shows that it’s a few bands into the surface. The minimum W/L required to break-even in the model turns out to be far lower, merely 52/48. Alternately, one could similarly say that at a 70/30 W/L the minimum RR required to break even is 1:2.

This of course is simply the tip of the iceberg. There are a variety of analyses and insights that can be conducted utilizing this application. Feel free to try it for yourself:

Monte Carlo Simulator

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