The Maths Every Day Trader Should Know
Should I take profit or let the winner run?
Compare banking a winner, taking partial profits, and leaving a runner through their complete outcome distributions rather than one memorable missed move.
By ContextChart Research · 4 min
Published
Compare the whole exit policy
Try it yourself
Increasing the target replays the same complete paths. Its chance of being reached is not held constant.
| Constructed path | Full exit | Partial + runner |
|---|---|---|
| +1.00R | +1.50R | |
| +1.00R | +0.50R | |
| -1.00R | -1.00R | |
| +1.00R | +0.80R | |
| +0.30R | +0.30R |
Mean across all five · full
+0.46R
Mean across all five · partial
+0.42R
Every path stays in the comparison, including the trade stopped before the later recovery.
Follow the continuation path
- Continuation
- Initial stop: -1
- Entry / remainder stop after +1: 0
- First target: 1
- Runner target: 2
Read the plotted values
| Illustrative time step | Continuation |
|---|---|
| 0 | 0 |
| 1 | 0.4 |
| 2 | 1.1 |
| 3 | 1.4 |
| 4 | 2 |
| 5 | 2.6 |
| 6 | 3 |
Select a path in the comparison table. Strong line: market path until the partial policy closes its final remainder. Faded line: later market movement. Markers show the exact first crossing of the straight segments.
| Policy event | Time step | Position closed | Price / initial R |
|---|---|---|---|
| Full exit · target | 1.86 | 100% | +1.00R |
| Partial · banked at first target | 1.86 | 50% | +1.00R |
| Partial · runner target | 4.00 | 50% | +2.00R |
Five equally weighted constructed paths, not an empirical distribution. Both policies start with a −1R stop. Full exit takes +1R; partial exit banks the chosen share at +1R, moves the remainder’s stop to entry, and seeks the runner target. Exact fills, no costs.
The idea
You take profit, and price keeps going. It is tempting to judge the decision by everything that happened afterward.
A useful comparison includes the other paths too: price reverses after the first target, the runner expires, or the trade never reaches the point where you would have taken a partial profit.
Banking part of a position and moving the rest to breakeven changes the shape of the outcome. Some gains become smaller but more secure. Other paths retain the chance of a larger payoff. Whether the average improves depends on how often each path occurs and what it pays after costs.
“Breakeven” also needs an accounting definition. Returning to the entry price does not necessarily return the position to zero after spread, commission, financing, and slippage.
The question therefore becomes measurable: for the same entry opportunities, how does each complete exit policy affect average outcome, variability, drawdown, and holding time?
An exit changes the distribution of outcomes; its value needs the whole record, including the trades that fail to continue.
How this experiment works
Compare an illustrative full exit with a partial exit and runner. Change the share banked and the runner target. Replay the same constructed paths and examine all the displayed outcomes together.
The five paths are teaching examples, not a measured distribution of future outcomes. A historical comparison would need to replay each exit rule on the same price paths. Moving a target farther away should not automatically retain its old probability of being reached.
How we use this
Our first runner study contained a counting error in the bar that reached the initial target. Correcting that error and checking minute bars materially changed the continuation results.
The audited comparison then showed that apparently attractive runner hit rates could be explained by barrier distances in the tested sample. The exit alternatives changed the spread of outcomes without demonstrating the claimed gain in their average.
That was a useful result: it replaced a feeling about money “left on the table” with a comparison we could inspect. It did not prove that every trailing or partial-exit policy is equivalent.
Show the maths
Conditional on reaching the first profit-taking point, suppose fraction a exits at t R. The remainder reaches u R with probability q, or exits at s R otherwise:
Conditional expected R = a × t + (1 − a) × [q × u + (1 − q) × s]
This expression omits further costs and timeouts. A full strategy comparison must also include trades that fail before reaching that first point.
What this does not establish
The best exit for one measured setup may differ from another. An attractive conditional return does not establish positive expectancy from entry. Keep the sample, timing assumptions, and transaction costs visible when testing the rule.