How long should a 6 pip stop and 9 pip target take to resolve? A random walk answer

[Fairman]

How long should a 6 pip stop and 9 pip target take to resolve? A random walk answer

There's a neat result for a driftless random walk with continuous prices, which is close to how stops and targets get hit by ticks. The average time until price touches either a stop a pips away or a target b pips away is a times b, divided by the variance of one step. With a stop of 6 and a target of 9, that's 54 divided by the squared size of a typical step in pips.

A step is whatever bar you use, and its size is the standard deviation of close minus previous close.
Standard deviation 1 pip per M5 bar: 54 bars, 4.5 hours.
1.5 pips: 24 bars, 2 hours.
2 pips: 13.5 bars, about 67 minutes.
3 pips: 6 bars, 30 minutes.

On M1 the step is smaller. At 0.7 pips per bar the same 6 and 9 takes about 110 bars, nearly two hours, which isn't what most people mean by a scalp.

Two things come out of it. First, scale: double the stop and the target and the time quadruples, it doesn't double. Second, volatility enters squared. If the London open takes your step size from 1.5 to 3 pips, the expected resolution time falls from 24 bars to 6.

To measure your own step size, take the last 200 closes at the hours you trade, compute close minus previous close, and take the standard deviation. Then compare what the formula says with the average hold time in your journal. If your trades take much longer, the stop and target are wide for how that pair actually moves in your window, or winners are being held longer than the plan says.

[FXS Prop Desk]

Fairman, the random walk result gives a useful baseline. If the actual time to resolution is much shorter than the formula predicts, the market was more volatile than assumed; if much longer, it was quieter. Comparing actual trade durations with the formula is a nice way to check whether a stop and target fit the current conditions. A big mismatch either way is a hint that the stop and target were sized for a different market than the one on screen.

[Fairman]

The formula gives an average, and the distribution is lopsided. I simulated Gaussian steps of 2 pips, checked at each bar close, for a 6 pip stop and 9 pip target. Because checking at closes overshoots the levels a little, the average came out at 18.5 bars rather than 13.5, and the median at 14 bars. About 5% of trades finished within 3 bars, 89% within 27 bars, and 97% within 40. So a few trades drift for a long time while most are done quickly. A time stop at roughly twice the formula's figure cuts only the tail, whereas one at the median would cut nearly half your trades before they resolve.

[Fairman]

Run it the other way to see why a five minute scalp on M1 is a cost problem. On M1 with a step of 0.7 pips, a typical hold of 5 bars means the stop times the target is about 5 times 0.49, so roughly 2.5. A 1.2 pip stop with a 2 pip target fits that. Both are smaller than most spreads. The maths says that if you want trades to resolve in a few minutes on M1, the distances are too small to survive costs, so either the holds are longer than a few minutes in practice or the strategy has a real drift that the random walk doesn't capture. Which of those applies to you is something your own data can answer.

[Amanhasnoname]

I tested this against my own journal on AUDUSD during the Sydney and Tokyo overlap and the formula was surprisingly close. My step size there on M5 was about 1.2 pips, which predicts roughly 37 bars for a 6 and 9 setup. My actual average hold on those trades was a little over three hours, so within shouting distance, and it explained why those trades always felt so slow.

The useful part was seeing the London numbers next to it. The same pair at 08:00 London had a step closer to 2.5 pips, which brings the expected time down to under ten bars. That matched my experience that the same setup resolved in about forty minutes there. It made me stop using a fixed time stop across sessions.

I now set my time stop at about twice the formula's estimate for the hour I'm trading. If a trade is still open past that, it usually means the market has gone quiet around my levels, and closing it at the market has saved me more than it has cost so far.

[Fairman]

You can also pick distances from the hold time you want. Say you want trades to resolve in about 6 M5 bars, and your step size at your hours is 2 pips. Stop times target should be about 6 times 4, so 24. A 4 pip stop with a 6 pip target fits, as does 5 and 5. Compare that with whatever stop and target you use now. If you're running 8 and 12, the product is 96 and the average resolution is around 24 bars, two hours, on this step size. It doesn't mean the setup is wrong, but the plan and the hold time should agree with each other.

[Fairman]

Two caveats. Volatility clusters, so the step size you measured over 200 bars may not hold for the next hour, and the time estimate moves with the square of that error. And the spread starts you nearer the stop. With a 0.8 pip cost, a long that enters at the ask effectively starts 0.8 pips closer to the stop and 0.8 further from the target. The stop is then 5.2 pips away and the target 9.8, which makes the product 51 instead of 54, hardly a change in time, but the chance of reaching the target first drops from 40% to 5.2 divided by 15, which is 34.7%. The cost matters more for odds than for duration.