30 day limit, 10% target, 0.5% risk at a 0.2R edge: the chance of finishing in time

[Fairman]

30 day limit, 10% target, 0.5% risk at a 0.2R edge: the chance of finishing in time

Suppose an evaluation gives 30 calendar days to make 10%. That is about 22 trading days. You risk 0.5% a trade, so the target is 20R. Your setup wins half the time at 1.4R and loses 1R otherwise, so the expectancy is 0.5 x 1.4 - 0.5 = +0.2R a trade. You take about 3 trades a day, 66 in all.

Average result after 66 trades: 66 x 0.2 = +13.2R, short of the 20R target. Spread of results: each trade has a standard deviation of 1.2R, so over 66 trades it is 1.2 x sqrt(66), about 9.75R. To reach 20R you need to be 6.8R above the average, which is 0.7 standard deviations. The chance is about 24%.

More trades change it quickly:
100 trades: mean 20R, chance about 50%
150 trades: mean 30R, SD 14.7R, chance about 75%
50 trades: mean 10R, SD 8.5R, chance about 12%

With a genuine edge this size, the clock can fail you more often than the market. This ignores the loss limits, which would remove some of the paths, so the true figure is somewhat lower.

My own sums, using a normal approximation.

[FXS HongKong Scalper]

The square root calculation shows how tight the timing is. With these numbers the chance of finishing in time is low, maybe 25 to 30%. Increasing risk raises the chance of hitting the target but also of breaching. Firms without time limits change the math considerably, which makes them more suitable for lower risk approaches.

[Fairman]

There are two ways to raise the chance: more trades or more risk per trade. Doubling risk to 1% halves the target to 10R. The mean after 66 trades is still 13.2R, now above the target, and the chance climbs to 1 - Phi((10 - 13.2) / 9.75), about 63%. But the daily and overall loss limits did not change, and at 1% a run of 5 losses is 5% and a run of 10 is 10%, which on a 10% max loss is the end. In other words, the clock pushes toward larger risk, and the loss limit pushes back. How the two balance depends on the edge, and a 0.2R edge is not forgiving.

[Fairman]

The number of trades is not free either. Taking 150 trades in 22 days is 6.8 a day, and unless the setup occurs that often, the extra trades are lower quality, which lowers the edge below 0.2R. Say the extra 84 trades have an expectancy of 0.05R instead. Then the mean is 66 x 0.2 + 84 x 0.05 = 17.4R, and the SD is about 1.2 x sqrt(150) = 14.7R, so reaching 20R has a probability of about 43%. Better than 24%, but far below the 75% the pure 150 trade calculation suggested. Trade count needs a setup that really repeats, and the honest figure for how many good setups a week produces comes from the journal.

[Fairman]

Edge size matters more than people expect. Keep 66 trades at 0.5% risk. With an edge of 0.3R the mean is 19.8R and the chance of reaching 20R is about 50%. With 0.1R, the mean is 6.6R, SD 9.75R, and the chance falls to 8%. So a 0.1R system at this pace almost never finishes in time, whatever it does on a longer horizon. Without a time limit the same edge would still get there, only later. A 30 day clock mostly rewards a stronger edge or luck. If you are sure of a small edge, the time limit is the cost to price in, and a programme that gives 60 days instead of 30 changes the picture a lot: at 132 trades the same 0.2R system has a mean of 26.4R and SD 13.8R, so the chance of reaching 20R is about 68%.

[Fairman]

To use this on your own numbers, you need three figures from your journal: the average R per trade, the standard deviation of R per trade, and how many trades you actually take in 22 days. In a spreadsheet, compute =(Target - N*Mean) / (SD*SQRT(N)) for the z score and =1-NORM.S.DIST(z,TRUE) for the chance. With Target 20, N 66, Mean 0.2, SD 1.2 the z score is 0.70 and the chance 0.24. Change N and Mean to see how sensitive it is. If the figure is below 30% you now know the programme's clock is the main obstacle, which is a better thing to find out before paying the fee.