Level I ยท Economics

Learning Module 8
Exchange Rate Calculations

Key Outcomes Summary & Practice Problems

Learning Outcomes

What you must be able to do

Curriculum Year: 2026

LOS 1

Calculate and interpret currency cross-rates.

LOS 2

Explain the arbitrage relationship between spot and forward exchange rates and interest rates, calculate a forward rate using points or in percentage terms, and interpret a forward discount or premium.

1 ยท Cross-Rate Calculations

    • Cross-Rate โ€” An exchange rate between two currencies that are not directly quoted. Derived from their quotes against a third currency (usually USD).

    • Calculation โ€” Use multiplication or inversion to cancel out the common currency.

    • Example โ€” To get CAD/EUR from CAD/USD and USD/EUR: multiply CAD/USD ร— USD/EUR.

    • Triangular Arbitrage โ€” Exploiting mispricing between cross-rates and the underlying quotes to earn riskless profit.

CROSS-RATE

If given A/B and B/C, then A/C = (A/B) ร— (B/C)
Invert if necessary to cancel currencies.

2 ยท Forward Rate Calculations

    • Forward Points (Swap Points) โ€” Difference between forward rate and spot rate, scaled to the last decimal of the spot quote (usually ร—10,000 for four-decimal quotes, ร—100 for yen).

    • Forward Discount/Premium โ€” If forward rate > spot, base currency is at a forward premium; if forward < spot, at a discount.

    • Covered Interest Rate Parity โ€” Forward rate is determined by interest rate differential: Ff/d = Sf/d ร— (1 + rfฯ„) / (1 + rdฯ„).

    • Forward Points as Percentage โ€” (F/S โ€“ 1) ร— 100.

    • Interpretation โ€” Currency with higher interest rate trades at a forward discount; lower interest rate at a premium.

COVERED INTEREST PARITY

Ff/d = Sf/d ร— (1 + rfฯ„) / (1 + rdฯ„)
Forward points = (F โ€“ S) ร— 10,000 (or 100 for yen).