The Maths Every Day Trader Should Know
Was one currency strong, or the other weak?
Understand why every FX pair contains two currencies, how their moves combine, and what a strength chart can and cannot tell you.
By ContextChart Research · 4 min
Published
Look through the pair to its two legs
Try it yourself
Pair’s log movement · base minus quote
+0.30%
+0.30% is the corresponding ordinary percentage price change.
Move both legs equally: the pair stands still. A pair that barely moves can contain two active currencies moving together.
+0.50% − (+0.20%) = +0.30% log movement. Equal movements cancel. Opposite movements add to the difference. These leg movements use the same basket reference.
Constructed relative log changes against the same basket reference. Log changes subtract exactly; this is currency arithmetic, not live strength or a directional forecast.
The idea
EURUSD falls. Did the euro weaken, the dollar strengthen, or both?
That pair alone cannot separate the explanations. It records how many dollars one euro buys. A change in either currency's value can change that exchange rate.
Other pairs add information. If the dollar rises against several currencies at the same time, the shared dollar movement becomes easier to distinguish from a euro-specific move. A basket-based strength chart collects those relationships into a consistent view.
“Strength” still needs a reference. A currency has no absolute exchange value floating outside all comparisons. Our research uses an explicitly defined currency basket. A different basket can produce a different account of relative strength.
This gives you a more informative description of the chart. It also helps explain why an apparent view on one currency can be poorly expressed through a particular pair. The other leg may move with it and cancel much of the difference, or move against it and amplify the pair's change.
A currency pair shows the difference between two relative values, so understanding both legs improves the description of its move.
How this experiment works
Change the illustrative movement of each currency separately. Watch the pair when the legs move together, when one stays still, and when they move in opposite directions.
The controls describe relative log movements. Equal movements cancel in the pair. Opposite movements add to the difference. These are constructed examples of the relationship, not current strength readings or forecasts.
How we use this
ContextChart's strength research built one mathematical representation for both historical and live prices. It helped us ask whose movement an FX pair records and how much of a currency view a particular expression retains.
The same research tested whether recent strength predicted subsequent direction. The tested persistence, fading, and agreement rules did not establish a robust after-cost advantage. A strength board can tell us what has happened without telling us what should happen next.
That distinction changed the role of the measurement: useful context needs an additional, tested reason before it becomes a directional trade.
Show the maths
For relative currency values on a common log scale:
Log pair price = base-currency value − quote-currency value
Log pair change = base change − quote change
Eight currencies contain seven independent relative degrees of freedom. Observing more of their pairs adds redundant information and measurement checks, rather than creating a new independent currency for every symbol.
What this does not establish
A decomposed move does not reveal the identity or motive of whoever traded. It also does not establish future direction or an automatically superior pair. Live quotes, costs, the chosen basket, and holding horizon matter. Continue with how several positions can become one underlying bet.