CFA Level I Exam · Capital Flows and the FX Market

Exchange Rate Quotations and Cross Rates Explained

Updated 7 October 2026 · Fact-checked

An FX quote is written A/B = x: one unit of the base currency A costs x units of the price currency B. Dealers quote a bid (they buy base) and an ask (they sell base). A cross rate is derived from two quotes sharing a common currency; if the market quote differs, triangular arbitrage exists.

Understand Exchange Rate Quotations and Cross Rates

An exchange rate is the price of one currency in terms of another. It is written A/B = x. A is the base currency and B is the price currency (also called the quote currency). The quote says one unit of A costs x units of B. So EUR/USD = 1.10 means €1 costs $1.10.

Direct and indirect quotes depend on your point of view. A direct quote has your domestic currency as the price currency. An indirect quote has your domestic currency as the base. For a US investor, EUR/USD = 1.10 is direct. For a euro-based investor, the same quote is indirect. Always ask: which currency is the domestic one? Flipping a quote just means taking the reciprocal: USD/EUR = 1 ÷ 1.10 = 0.9091.

Dealers quote two-sided prices. The bid is the price at which the dealer buys the base currency from you. The ask (offer) is the price at which the dealer sells the base currency to you. The ask is always higher than the bid. The difference is the bid-ask spread, the dealer's compensation. Spreads are often expressed in pips, the last decimal place quoted. The bid and ask always refer to the base currency, whatever your own domestic currency is.

A cross rate is an exchange rate between two currencies calculated from each one's rate against a third. If you know A/C and B/C, you can find A/B. Line up the quotes so the common currency cancels. If the quoted cross rate in the market does not match the calculated one, a risk-free profit is possible through triangular arbitrage: three trades that start and end in the same currency.

With bid-ask quotes, cross rates also have a bid and an ask. You must use the side that works against the dealer on each leg, which is why the cross bid is lower and the ask higher than a simple midpoint calculation. When you multiply two quotes, pair bid with bid and ask with ask. When you divide, pair the bid of the numerator quote with the ask of the denominator quote, and the ask of the numerator quote with the bid of the denominator quote.

Key formulas to remember

Quote convention: A/B = x means 1 A = x B; A is the base currency, B is the price currency. The quote tells you the price of one unit of the base.
Inverse quote: B/A = 1 ÷ (A/B); Use this to flip a quote. With bid-ask: bid(B/A) = 1 ÷ ask(A/B) and ask(B/A) = 1 ÷ bid(A/B).
Bid-ask spread: Spread = ask − bid; Spread as a percentage is (ask − bid) ÷ ask or ÷ midpoint, depending on the question; follow the wording.
Cross rate, same base: A/B = (A/C) ÷ (B/C); Both quotes share the same price currency C, so it cancels by division.
Cross rate, base meets price: A/B = (A/C) × (C/B); C is the price currency of one quote and the base of the other, so it cancels by multiplication.
Cross-rate bid and ask (multiplication): A/B bid = (A/C bid) × (C/B bid); A/B ask = (A/C ask) × (C/B ask); Apply when both quotes are set up for multiplication. If you must divide, use the division rule below or invert the other quote first using the inverse bid-ask rule.
Cross-rate bid and ask (division): For A/B = (A/C) ÷ (B/C): bid(A/B) = bid(A/C) ÷ ask(B/C); ask(A/B) = ask(A/C) ÷ bid(B/C); Both quotes share the same price currency C. The lowest cross bid divides the lowest numerator by the highest denominator; the highest cross ask does the reverse.

How to solve Exchange Rate Quotations and Cross Rates questions

Use this method for any question on quotes, spreads, cross rates or triangular arbitrage.

1Write each quote as A/B and label the base (A) and the price (B). Read the question for which currency is domestic.
2Decide what you are doing: buying or selling the base currency. You buy the base at the ask and sell the base at the bid.
3If the quote is the wrong way round, invert it. When inverting a bid-ask pair, the new bid is 1 ÷ old ask and the new ask is 1 ÷ old bid.
4For a cross rate, arrange the two quotes so the common currency cancels. Multiply or divide accordingly.
5For triangular arbitrage, compute the implied cross rate from the two given quotes and compare it with the quoted cross rate.
6Start with a currency, trade around the triangle, and finish in the starting currency. Follow each leg with the correct bid or ask. Profit = final amount − starting amount.
7Check the sign: the dealer always gets the better side. If your answer shows you gaining from the spread on a single trade, recheck.

Quickest way: Cancel-the-currency shortcut

When to use it: Use it for mid-rate cross rates and for deciding whether an arbitrage exists, when options are numbers listed smallest to largest.

Write the unit labels, for example (USD per EUR) × (JPY per USD).
Multiply so the unwanted currency cancels and the units left are the ones you want (JPY per EUR).
If a unit does not cancel, flip one quote and try again.
Compare the implied cross with the quoted cross. If the quoted base is priced higher than implied, sell it in the market and buy it through the other route.
Eliminate options with the wrong direction (for example a result above 1 when the cross must be below 1) before doing the arithmetic.

Common mistakes in Exchange Rate Quotations and Cross Rates

Treating the first currency as the one you receive or pay in, instead of the base.
The slash looks like a division sign, so students read A/B as A divided by B in the wrong way round.
Fix: Read A/B = x as 1 A costs x B. The price is always in the second currency.
Using the bid when buying the base currency.
Students think of the bid as the price they bid, rather than the price the dealer bids.
Fix: Bid and ask are from the dealer's view. You buy the base at the ask and sell it at the bid.
Inverting a bid-ask quote by inverting the bid to get the new bid.
It looks natural to invert each number in place.
Fix: The new bid is 1 ÷ old ask and the new ask is 1 ÷ old bid. The ordering flips because the dealer's buying and selling swap.
Mixing up direct and indirect quotes without checking the domestic currency.
Students memorise that EUR/USD is direct, but that is true only for a USD-based person.
Fix: Ask which currency is domestic. If it is the price currency, the quote is direct. If it is the base, indirect.
Multiplying two quotes when the common currency does not cancel.
Students multiply without writing units.
Fix: Write the units. If the common currency appears on the same side in both quotes, invert one quote first.
Stopping triangular arbitrage after two legs or not ending in the starting currency.
The third leg feels like a repeat of the first.
Fix: Always close the loop. Profit is only measured in the currency you started with.

Worked examples

Example 1

A dealer quotes USD/EUR = 0.9000 / 0.9010 (bid / ask) and EUR/GBP = 0.8500 / 0.8512. Calculate the bid and ask for USD/GBP. Which of the following is the closest ask rate? A) 0.7650 B) 0.7669 C) 0.7688

Show the solution

USD/GBP = (USD/EUR) × (EUR/GBP). EUR cancels, so you multiply.
Bid = 0.9000 × 0.8500 = 0.7650.
Ask = 0.9010 × 0.8512 = 0.76693 (0.9010 × 0.8512: 0.9 × 0.8512 = 0.76608; 0.001 × 0.8512 = 0.00085; total 0.76693).
The ask is about 0.7669.

Answer: B) 0.7669. The USD/GBP quote is about 0.7650 / 0.7669.

Example 2

Spot quotes: USD/EUR = 0.8000, GBP/USD = 1.2500 and GBP/EUR = 0.9800. You hold USD 1,000,000. Using mid-rates, does triangular arbitrage exist, and what is the profit if you start in USD? A) USD 0 B) USD 20,408 C) USD 25,000

Show the solution

Implied GBP/EUR = (GBP/USD) × (USD/EUR) = 1.2500 × 0.8000 = 1.0000.
The quoted GBP/EUR is 0.9800, lower than the implied 1.0000. So GBP is cheap in EUR in the market quote, and arbitrage exists.
Leg 1: Convert USD 1,000,000 to EUR at USD/EUR = 0.8000: EUR 800,000.
Leg 2: Use EUR to buy GBP at the quoted GBP/EUR = 0.9800: EUR 800,000 ÷ 0.9800 = GBP 816,326.53.
Leg 3: Convert GBP to USD at GBP/USD = 1.2500: 816,326.53 × 1.25 = USD 1,020,408.16.
Profit = 1,020,408.16 − 1,000,000 = USD 20,408 (rounded to the nearest dollar).

Answer: B) USD 20,408. Arbitrage exists because the quoted GBP/EUR of 0.9800 is below the implied 1.0000.

Exam tips

Write the quote as 1 base = x price on your scratch paper before anything else. It prevents most direction errors.
Numerical options are listed from smallest to largest. Estimate the cross rate roughly first; often two options are on the wrong side of 1 and can be removed.
Bid and ask are always the dealer's view and always for the base currency. Check this whenever a question asks what you pay or receive.
For arbitrage questions, find the mispriced cross first, then trade the loop. You do not need to guess the direction; the numbers tell you.
Spreads are usually reported in pips or as a percentage. Read the question for which one before you calculate.

Practice questions from Capital Flows and the FX Market

Exchange Rate Quotations and Cross Rates 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 Quotations and Cross Rates: frequently asked questions

How do I calculate cross rates for CFA Level I?

Write both quotes with units, then arrange them so the common currency cancels. Multiply if it is the price in one and the base in the other. Divide if it is the same in both. With bid-ask quotes, multiplying pairs bid with bid and ask with ask, while dividing pairs the bid with the other quote's ask and the ask with its bid.

What is the difference between a direct and an indirect quote?

A direct quote has your domestic currency as the price currency, so it shows how much domestic currency one foreign unit costs. An indirect quote has your domestic currency as the base. The same quote can be direct for one investor and indirect for another.

What is the difference between bid and ask in an FX quote?

The bid is the price at which the dealer buys the base currency. The ask is the price at which the dealer sells it. The ask is higher than the bid, and the difference is the dealer's spread.

How does triangular arbitrage work?

You compare the market cross rate with the one implied by two other quotes. If they differ, you trade through three currencies and end in the starting currency. The profit is the difference between the final and starting amounts, with no risk if quotes hold.