The Maths Every Day Trader Should Know
Are these really separate bets?
Reveal the shared currency and market exposures behind multiple positions, and see why a busy trade list can still depend on one event.
By ContextChart Research · 4 min
Published
Count the idea behind the tickets
Try it yourself
Open tickets
2
Net USD direction
-2 units
Teal links add a currency leg; red links subtract one. Opposite legs cancel in this simplified tally. USD is outlined to make the shared dollar direction visible.
| Currency leg | Net directional units |
|---|---|
| EUR | +1 |
| GBP | +1 |
| USD | -2 |
Ask which currency movement would hurt several positions together. Netting opposite legs can hide gross exposure and does not establish independent trade outcomes.
Each selected position contributes one simplified base-currency unit and the opposite quote-currency unit. These are directional bookkeeping units, not cash exposure, margin, covariance, or a portfolio-risk estimate.
The idea
Five open positions can depend on one market view.
Buying EURUSD and GBPUSD gives you different symbols, but both positions contain a short-dollar exposure. Selling USDCHF adds another way for dollar strength to hurt. The trade list has grown faster than the number of underlying ideas.
This matters because outcomes that arrive together can create a larger account loss than a series of isolated trades. Spreading positions across symbols does not automatically spread the economic risk.
There are several useful views of that risk. Shared trade reasoning can reveal that positions came from one thesis. Currency legs reveal direct exposures. Historical co-movement reveals broader relationships. Actual stop and target outcomes reveal whether trades lose together along the path.
These views complement each other. Two instruments can have modest return correlation while their trading rules still cause losses during the same kind of event. Relationships can also change across horizons and market conditions.
Count the sources of loss behind the positions as well as the positions themselves.
How this experiment works
Add and remove positions in the illustrative basket. Look at the currency legs behind each symbol and compare the resulting shared exposure with the number of tickets.
Then ask which market movement would hurt several positions at once. The demonstration uses simplified equal exposure units. A real portfolio also needs contract values, position sizes, cash conversions, and the behaviour of its exits.
How we use this
Our declustering research compared shared-currency relationships, instrument groups, and simulated trade outcomes. It found important overlap between apparently separate trades, while also showing that broad labels such as “FX” or “commodities” were too crude to describe every relationship.
The research helped us treat expression and portfolio exposure as separate decisions. A useful market view does not become several independent discoveries because it can be traded through several pairs.
The measured number of independent directions was specific to the sample, universe, horizon, and method. It is not a permanent limit on how many ideas markets can contain.
Show the maths
For weighted returns, portfolio variance includes each position's variance and the covariance between every pair of positions:
Portfolio variance = sum of weighted individual variances + sum of weighted pairwise covariances
If two positions move together, the covariance terms add risk. If they offset, those terms can reduce return variance. The result depends on actual weights and relationships.
Net currency exposure is another useful view, but netting a currency does not remove every source of risk. Stop-outs, changing prices, financing, and imperfect hedges can make the realized path different from a simple exposure sum.
What this does not establish
Diversification can reduce some risks without improving the expected return of the underlying trades. Historical correlation is also an estimate, not a contract about future behaviour. Use the exposure view to ask better questions about the account's whole path.