Library/CFA (Chartered Financial Analyst)/ECONOMICS: CFA® Program Curriculum 2026 • LEVEL I • VOLUME 2/Learning Module 8 Exchange Rate Calculations

Learning Module 8 Exchange Rate Calculations

50 questions available

Take a quiz Listen to a podcast

Cross-Rate Construction and Quoting Conventions5 min

This chapter explains how to calculate exchange rate cross-rates and how forward exchange rates relate to spot rates and interest rates through arbitrage relationships. Cross-rates: Given two exchange rates involving three currencies, you can derive the third by algebraic cancellation. When currency A/B and B/C are known, A/C equals (A/B) times (B/C) after appropriate inversions so that the intermediary currency cancels. The professional FX market uses standard quoting conventions (for example USD/EUR, CAD/USD, JPY/USD) and often requires inverting a quoted pair to form a cross-rate. Yen rates are typically quoted with two decimals; most other major pairs use four decimals. Market efficiencies and high-frequency trading make mispriced cross-rates rare; if inconsistent cross rates are quoted, triangular arbitrage (buy low, sell high across three pairs) will quickly remove the discrepancy. Forward quotes and points: Forward exchange rates are usually displayed as forward points (pips), the difference between the forward and spot rates scaled to match the last decimal place of the spot quote (multiply by 10,000 for four-decimal pairs and by 100 for yen-style two-decimal pairs). A positive forward points value (forward > spot) means the base currency trades at a forward premium; a negative value indicates a forward discount. Forward points generally increase in absolute terms with maturity and with the size of interest rate differentials. Converting forward points to a forward rate requires dividing the quoted points by the scaling factor and adding to the spot rate; conversely, a quoted forward rate can be expressed as points by subtracting spot and scaling. Percentage representation of forward premia/discounts is calculated as (F/S) - 1, where F is forward and S is spot.

Key Points

Cross-rates are computed by multiplying two rates and inverting as needed so intermediary currency cancels.
Standard market conventions mean many quotes are USD-based; yen quotes use two decimals.
Forward points are scaled differences (pips) between forward and spot; scale is 10,000 for 4-decimal pairs, 100 for yen-style pairs.
Positive points => base currency forward premium; negative => forward discount.

Covered Interest Parity and Forward Rate Formula5 min

Key Points

Covered interest parity equates domestic deposit returns to hedged foreign deposit returns.
Forward rate formula: F_f/d = S_f/d * ((1 + r_f) / (1 + r_d)) for whole-period rates.
For short maturities use fractional term tau: (1 + r * tau) with correct day count.
Currency with higher interest rate will trade at forward discount (after careful attention to quote convention).

Practical Forward Calculations and Interpretation5 min

Key Points

Use day-count conventions (e.g., actual/360) when computing tau for Libor-style rates.
Forward points scale with both maturity and interest rate differentials; doubling differential roughly doubles points.
Triangular arbitrage profit equals mispricing times transaction size (ignoring costs).
Forward rates are set to eliminate riskless arbitrage; they should not be relied on as accurate point forecasts of future spot rates.

Questions

Question 1

Given USD/EUR = 1.2500 and CAD/USD = 0.8000, what is the CAD/EUR cross-rate?

Learning Module 8 Exchange Rate Calculations

Questions

Other chapters