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CFA Level I · CFA Level I Exam

Exchange Rate Calculations for CFA Level I

Exchange rate calculations cover how currency prices are quoted and converted: price and base currency, bid-ask spreads, cross rates, forward rates from interest rate differentials, and percentage change in a currency's value. You solve them by fixing the quote direction first, then multiplying or inverting carefully, and checking that the answer makes sense.

What this chapter covers

This chapter teaches you the arithmetic of currency markets. You start with how a quote works: in a price/base quote such as EUR/USD = 1.0850, one unit of the base currency (EUR) costs 1.0850 units of the price currency (USD). Every later calculation depends on reading this correctly.

From there you move to dealer quotes (bid and offer, and the spread between them), cross rates built from two other pairs, and triangular arbitrage when the quoted cross rate does not match the implied one. Then you build forward rates using covered interest rate parity and forward points, and finish with percentage change in the value of a currency, where the base versus price direction decides the sign.

The chapter connects to the rest of the paper in several places. It supports the Economics topic on currency exchange rates and parity conditions, Fixed Income and Portfolio Construction when returns are converted across currencies, and Derivatives when you price currency forwards. Questions are standalone three-option MCQs, so you need fast, error-free method more than theory.

Exchange rate questions are mechanical, which makes them some of the most reliable marks in the paper once your method is fixed. Economics (6-9% in the 2027 curriculum) covers currency exchange rates, and related skills also appear in Derivatives and Portfolio Construction, whose weights are listed separately. Most lost marks come from inverting the wrong way or using the wrong side of a bid-ask quote, not from hard maths. With no penalty for wrong answers and about 90 seconds per question, a clean routine saves time you can spend on harder items.

Exchange Rate Calculations: topics in the order to study them

  1. 1Exchange Rate Quotations and TerminologyEverything else depends on reading price currency, base currency and direction correctly, so learn it first.
  2. 2Bid-Ask Spreads and Dealer QuotesOnce you can read a quote, learn that dealers show two prices and which side you trade at.
  3. 3Cross Rates and Triangular ArbitrageIt builds on quotes and bid-ask sides, because correct cross rates need the right bid and offer.
  4. 4Percentage Change in Currency ValueIt is short and uses only quote direction, so it is easy to learn before the forward material and gives you a quick win.
  5. 5Forward Rates, Points and Covered Interest ParityIt comes last because it needs quotes, direction and percentage thinking, plus interest rates for both currencies.

How to prepare Exchange Rate Calculations

Treat this chapter as a skill to drill, not a text to read. Short daily practice on a phone works well, with calculator keystrokes done by hand.

  1. Write the quote convention in your own words: price currency per one unit of base currency. Say it aloud for three pairs until it is automatic.
  2. For every problem, first label the base and price currency, then decide if you must multiply or divide. Write the units on each number so they cancel.
  3. Practise bid-ask by asking one question: which side of the dealer's quote would I trade at? You buy the base at the offer and sell it at the bid.
  4. Do cross rates and triangular arbitrage as a chain of conversions. Start with a currency amount, convert step by step, and compare the end result with the start.
  5. For forwards, memorise F = S × (1 + i price × T) ÷ (1 + i base × T) with the price currency rate on top and the base currency rate below. Check that the currency with the higher rate trades at a forward discount.
  6. Finish each session with 10 to 15 standalone MCQs. For each, eliminate the two options that come from inverting the wrong way or using the wrong bid or offer, then confirm the last one.
  7. Revise using a one-page sheet of formulas and common traps, and redo missed questions after a few days.

Common mistakes in Exchange Rate Calculations

  • Multiplying when you should divide (or the reverse) when converting between currencies.

    Fix: Write the units on every figure and make sure they cancel. With EUR/USD = 1.0850 (USD per EUR), a USD amount ÷ 1.0850 gives EUR. Multiplying the USD amount by 1.0850 gives the wrong unit, not EUR.

  • Using the bid when you should use the offer, or using the wrong side after inverting.

    Fix: Remember you buy the base at the offer and sell it at the bid. When inverting, new bid = 1 ÷ old offer and new offer = 1 ÷ old bid.

  • Placing the interest rates the wrong way round in the forward formula.

    Fix: Price currency rate goes on top, base currency rate below. Then sanity-check: the higher-rate currency should be at a forward discount.

  • Treating forward points as a full rate, or mis-scaling them.

    Fix: Convert points to a decimal first using the quote's scaling (for example 25 points = 0.0025 when points are in 1/10,000), then add to spot. Check the answer is close to spot.

  • Assuming the percentage change in one currency is the negative of the other's.

    Fix: Compute each side separately. If the base rises by 10% in price/base terms, the price currency falls by 1 − 1 ÷ 1.10, about 9.09%, not 10%.

  • Declaring an arbitrage because mid rates differ, ignoring the spread.

    Fix: Run the full conversion loop at the correct bid or offer for each leg and see whether you end with more than you started.

Last-day revision: Exchange Rate Calculations

  • A quote A/B = x means 1 unit of A (base) costs x units of B (price).
  • To invert a quote, take 1 ÷ x and swap the currency order.
  • Bid is the price at which the dealer buys the base currency; offer (ask) is where the dealer sells it.
  • You, the client, sell the base at the bid and buy the base at the offer.
  • Spread = offer − bid; it is the dealer's compensation and is wider for less liquid pairs.
  • Inverting a bid-ask quote: the new bid is 1 ÷ old offer and the new offer is 1 ÷ old bid.
  • Cross rate: A/C = (A/B) × (B/C); check that the middle currency cancels.
  • Triangular arbitrage exists when the quoted cross rate differs from the implied one after using the correct bid and offer sides.
  • Forward rate (price/base) F = S × (1 + i price × T) ÷ (1 + i base × T), using the same simple-interest convention as the question.
  • Forward points are F − S scaled by the quote's convention (usually 1/10,000, with 1/100 for JPY pairs); convert them back to a decimal correctly before adding to spot.
  • The currency with the higher interest rate trades at a forward discount under covered interest parity.
  • Base currency % change = (new spot ÷ old spot) − 1 for a price/base quote. Price currency % change = (old spot ÷ new spot) − 1 = 1 ÷ (1 + Δbase) − 1, which is not simply the negative of the base change.

Exchange Rate Calculations practice questions

Exchange Rate Calculations in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Exchange Rate Calculations: frequently asked questions

How do I know which currency is the base currency?

In a quote written A/B, A is the base currency and B is the price currency. The number tells you how many units of B you pay for one unit of A. Read the quote that way every time before you calculate.

How is a cross rate calculated for CFA Level I?

You chain two quotes so the common currency cancels. For example, to get EUR/GBP from EUR/USD and GBP/USD, divide EUR/USD by GBP/USD. With bid-ask quotes, use the bid and offer sides that match the trade you are making.

How do I find a forward exchange rate?

Use covered interest rate parity: F = S × (1 + i price × T) ÷ (1 + i base × T) for a price/base quote. Use the interest rates for the same period as the forward, in the compounding convention the question uses. The currency with the higher interest rate will be at a forward discount.

Do I need my calculator for these questions?

Usually basic arithmetic on a TI BA II Plus or HP 12C is enough. Use the reciprocal key for inversions, for example on the BA II Plus press the number then 2nd and the x⁻¹ key (labelled 1/x). Work to at least four decimal places so rounding does not push you to the wrong option.