Free lesson · Trading different assets

Foreign exchange: two currencies, one quote and financing

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Start with the idea

An FX quote tells you how much of the quote currency buys one unit of the base currency. Buying the pair means increasing base-currency exposure relative to quote currency.

Symbols, units & horizon

q_B: signed base-currency units
S_0,S_1: quote currency per one base unit at entry and exit
C_Q: net costs in quote currency, assumed nonnegative here
δ: specified quote increment per base unit
Π_Q: profit in quote currency
example base EUR and quote USD

When and why to use this

Use currency-aware units for FX signals, international portfolio exposures and hedges.

In a quote of 1.10 USD per EUR, EUR is the base and USD the quote. Buying 10,000 EUR creates a position worth $11,000 at that reference rate. A positive EUR/USD move benefits a long EUR position when measured in USD. If the account is in another currency, P&L needs a separate conversion.

Distinguish deliverable spot, forwards, exchange-traded currency futures and broker rolling-spot or CFD products. A CFD is a cash-settled contract with a provider, not ownership of the referenced currency or security. Overnight financing, quote conventions and counterparty terms differ. Not every account or jurisdiction permits every wrapper.

A pip is a conventional quote increment, but decimal precision varies across pairs and products. Calculate pip value from the actual quote increment and base-unit quantity, rather than assuming a universal lot or pip value.

For a strategy, examine sessions, spread widening, calendar events, settlement and roll charges. FX carry reflects financing and exchange-rate risk; an interest-rate differential does not guarantee a positive currency return. Research quote quality and synchronized timestamps before testing cross-pair relationships.

Π_{Q} = q_{B} (S_{1} - S_{0}) - C_{Q}, {pip value}_{Q} = | q_{B} | δ

Model assumptions, derivation and arithmetic

Foreign exchange: two currencies, one quote and financing

Subtract the two exchange rates to obtain quote-currency change per base unit.
Multiply by signed base units, then subtract costs in that same quote currency.
For a one-pip move, use δ as the rate change. Convert the resulting P&L separately if the account currency differs.

Work it by hand

Long 10,000 EUR from 1.1000 to 1.1050 USD/EUR gains 10,000×.005=$50 before $4 costs, or $46. With δ=.0001, one pip is $1 for this quantity.

Apply it in a strategy

Identify base, quote, account currency and product wrapper.
Translate intended exposure into base units with explicit increment and financing conventions.
Test session-aware fills and cash conversions before comparing carry, momentum or macro signals.

Research deliverable

Translate an FX ticket into base holdings, quote-currency cash flows and account-currency P&L.

Contract conventions · checked 12 September 2026

The arithmetic follows base/quote units. A futures quote can use a different convention from its related OTC currency pair; resolve that from the actual contract.

Further reading: CME · Understanding FX quote conventions ↗

Python implementation

Self-contained teaching example. Python 3.10+; dependencies and input conventions are shown in the code and notation. Run in your own Python environment.

def fx_profit(base_units,entry,exit,cost_quote=0,pip=.0001):
    if entry<=0 or exit<=0 or pip<=0 or cost_quote<0: raise ValueError("Invalid FX inputs")
    return base_units*(exit-entry)-cost_quote,abs(base_units)*pip

print(fx_profit(10000,1.1,1.105,4))

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