The Maths Every Day Trader Should Know
Is the market moving, or just moving around?
Separate volatility, displacement, path efficiency, and trading friction so a lively chart becomes easier to read.
By ContextChart Research · 4 min
Published
Movement, or movement around?
Try it yourself
- A · Steady route
Read the plotted values
| Observation | A · Steady route |
|---|---|
| 0 | 0 |
| 1 | 0.1 |
| 2 | 0.2 |
| 3 | 0.3 |
| 4 | 0.4 |
| 5 | 0.5 |
| 6 | 0.6 |
| 7 | 0.7 |
| 8 | 0.8 |
| 9 | 0.9 |
| 10 | 1 |
Total distance travelled
1.00 units
Final displacement
1.00 units
Displacement ÷ distance travelled
100.0%
Every path has the same overall range. This measure asks a different question.
Constructed paths with the same 1-unit high–low range. Efficiency describes this sampled route; it does not predict the next route or determine an executable stop.
The idea
A market can travel a long distance and end near where it began. It can also move in two clear legs that offer distinct opportunities, even if the session finishes flat.
Those paths deserve different descriptions. Volatility concerns the scale of movement. Displacement is the distance from the starting point to the ending point. Path efficiency compares that progress with the total travel between them.
Imagine walking to a shop. One route takes you steadily along the street. Another repeatedly doubles back. Both can finish at the same shop, but one route requires much more travel.
On a chart, that distinction depends on the clock you use. A path that looks smooth in hourly closes can contain large minute-by-minute reversals. A flat session can contain two sustained trends. One summary number cannot preserve all those features.
The useful question is specific: what does the path do at the scale relevant to this decision? Then ask what trading that path would cost.
Movement size, directional progress, and the cost of trading the path are separate properties.
How this experiment works
Compare constructed price paths with similar overall ranges. Change which path is displayed and examine the distance travelled, final displacement, and efficiency.
Before looking at the numbers, decide how you would describe each path. Then check whether the measure captures the feature you noticed. If two visibly different paths receive the same score, identify which information the score discarded.
How we use this
Our FX-noise study compared several measures rather than declaring one universal noise indicator. It examined persistence, reversals, efficiency, and the experience of simulated trades.
The extremes of some rankings persisted across sample halves. Middle rankings were less stable. Much of the difference in after-cost trade outcomes also came from spread relative to movement, rather than a special pattern of stop-outs.
That helped us separate a chart description from a trade recommendation. A measure can describe a market property without predicting whether the next trade wins. The study's cleanest and noisiest days did not supply a dependable next-trade advantage in the tested comparison.
Show the maths
For observed prices P0 through Pn:
Displacement = absolute value of (Pn − P0)
Path length = sum of absolute changes between successive observations
Efficiency = displacement ÷ path length
For a nonzero path, this ratio lies between zero and one. An entirely unchanged path needs its own defined handling because the denominator is zero. Sampling more frequently can reveal travel that coarse observations miss.
What this does not establish
A low efficiency score does not prove a market is untradeable. A high score does not establish a predictable continuation. Name the path feature, clock, and cost separately. That makes the next question—whose movement the chart represents—much easier to investigate.