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CFA® Level I · Economics · free lesson
Exchange Rate Calculations
Currency arithmetic is easy to get wrong under exam pressure: one inverted quote and every later number is off. This module drills the core calculations: reading quotes and measuring how much a currency has appreciated or depreciated, building cross rates, turning forward points into outright forward rates and premiums, and using covered interest rate parity to price forwards and spot arbitrage.
What you will learn
1. Interpret exchange rate quotes in terms of price and base currencies, distinguish direct from indirect quotes, and calculate the percentage change in one currency relative to another.
- A/B = units of A (price currency) per one unit of B (base currency).
- Direct quote = domestic currency per unit of foreign currency; indirect quote = its reciprocal.
- Base currency change = S1 / S0 - 1; price currency change = S0 / S1 - 1.
- Appreciation of one currency is not the same percentage as the depreciation of the other.
- Always check which currency is the base before calculating.
2. Calculate cross exchange rates from two quotes that share a common currency, and recognize when a quoted cross rate allows triangular arbitrage.
- A cross rate combines two quotes against a common currency.
- Arrange the quotes so the common currency cancels: A/B = A/C x C/B.
- Multiply when the common currency is base in one quote and price in the other; divide when it is in the same position in both.
- Check the answer for reasonableness against the two quotes.
- Gaps between quoted and implied cross rates create triangular arbitrage.
3. Calculate outright forward rates from forward points and calculate and interpret a forward premium or discount, including on an annualized basis.
- Forward rate = spot + points / 10,000 (points / 100 for two-decimal quotes such as JPY).
- Positive points: base currency at a forward premium; negative points: base at a discount.
- Premium or discount on the base currency = F / S - 1; annualize with 360 / days.
- The price currency has the opposite status to the base currency.
- Points reflect interest rate differentials, not expected spot moves.
4. Explain covered interest rate parity and the arbitrage that enforces it, and use it to calculate forward rates, forward points and arbitrage profits.
- Covered interest parity: F(P/B) = S(P/B) x (1 + i_P x days/360) / (1 + i_B x days/360).
- The higher-interest-rate currency trades at a forward discount.
- Forward points widen with the rate differential and the maturity.
- Quoted forward above parity: borrow the price currency, buy base spot, invest, sell base forward (and vice versa).
- Covered parity is enforced by arbitrage; it is not a forecast of future spot rates.
Module at a glance
- A/B = units of A (price currency) per one unit of B (base currency); check the base before calculating.
- Base currency change = S1 / S0 - 1; price currency change = S0 / S1 - 1; they are not mirror images.
- Cross rates: cancel the common currency; multiply or divide accordingly and sanity-check the result.
- Forward = spot + points / 10,000 (points / 100 for yen-type quotes).
- Positive points = base currency at a forward premium; negative = discount.
- Covered parity: F = S x (1 + i_P x days/360) / (1 + i_B x days/360).
- The higher-interest-rate currency trades at a forward discount.
- Forward above parity: borrow the price currency, buy and invest the base, sell it forward.
This free module has 4 lessons, 13 practice questions with full explanations.