Updated for the 2026-2027 CFA® Level I curriculum.
An exchange rate quote is meaningless until you know which currency is being priced and which currency is doing the pricing. This note teaches quotation discipline, the distinction between nominal and real exchange rates, and how to calculate the percentage change in a currency relative to another currency. These three skills work together on the exam. A single reversed sign or flipped quote can turn a correct answer into a wrong one.
Quick Answer
The nominal exchange rate vs real exchange rate distinction comes down to price levels.
The nominal rate is the quoted market rate: units of price currency per one unit of base currency.
The real exchange rate adjusts that quote for relative price levels between the two countries, showing the change in purchasing power rather than just the currency price.
To calculate a currency's percentage change, use (new quote − old quote) / old quote, and always confirm which currency sits in the numerator before interpreting the result.
Key Takeaways
A currency quote has two sides: the base currency (the one unit being priced) and the price currency (the units needed to buy it).
Direct quotes are written as price currency per one unit of base currency, shown as S(P/B).
The nominal exchange rate is the observed market quote with no price-level adjustment.
The real exchange rate adjusts the nominal rate for relative price levels: q(d/f) = S(d/f) × P(f) / P(d).
Percentage change in a currency uses (S1 − S0) / S0, applied to a clearly defined quote.
A rising S(P/B) quote means the base currency appreciated and the price currency depreciated.
Percentage changes calculated from a reciprocal quote are not the exact negative of the original change.
What You Need to Know for CFA Level I
Label every quote by units before doing any calculation.
Apply and keep the sign consistent with the quote's orientation.
Read a rising price-currency-per-base quote as base appreciation and price-currency depreciation.
Calculate or interpret a real exchange rate only after defining domestic and foreign price levels.
Recognize that flipping a quote to its reciprocal changes the percentage-change math, not just the sign.
How to Read an Exchange-Rate Quote
Every exchange rate has two currencies attached to it: a base currency and a price currency. The base currency is the one unit being measured. The price currency tells you how many units it takes to buy that one unit.
The standard notation is:
Where:
= price currency (the currency used to state the price)
= base currency (the currency being priced, always one unit)
= the spot exchange rate quote
If = 1.10, that means 1.10 USD buys 1 EUR. USD is the price currency. EUR is the base currency.
Every quote also has a reciprocal. Taking the reciprocal of gives , or how many euros it takes to buy one dollar. The reciprocal is . Do not assume slash notation is self-explanatory on the exam. Always confirm which currency is on top.
Nominal vs Real Exchange Rates
The nominal exchange rate is the rate you see quoted in the market. It reflects the current price of one currency in terms of another, with no adjustment for inflation or relative price levels.
The real exchange rate strips out the effect of price-level changes so you can see how the purchasing power of one currency has moved relative to the other. The formula, using domestic currency (d) as the price currency and foreign currency (f) as the base currency, is:
Where:
= real exchange rate, domestic currency per unit of foreign currency
= nominal exchange rate, domestic currency per unit of foreign currency
= foreign price level (a price index)
= domestic price level (a price index)
If and are equal, the real rate equals the nominal rate. If foreign prices rise faster than domestic prices, rises, and the real rate rises above the nominal rate for a given nominal quote. This means foreign goods have become relatively more expensive after adjusting for price-level changes, even if the nominal exchange rate has not moved.
This note keeps the real-rate discussion focused on the calculation and interpretation. Purchasing power parity theory, which explains why real rates move toward equilibrium over time, is covered elsewhere.
Currency Appreciation and Depreciation
Once a quote is defined, appreciation and depreciation follow directly from whether the quote rises or falls.
Quote Change | Base Currency (B) | Price Currency (P) |
|---|---|---|
rises | Appreciates | Depreciates |
falls | Depreciates | Appreciates |
If rises from 1.10 to 1.15, it now takes more dollars to buy one euro. The euro (base currency) appreciated. The dollar (price currency) depreciated. This also means European exports priced in dollars become more expensive for US buyers, while US exports priced in euros become cheaper for European buyers.
Trade-flow effects are covered in more depth on a separate note. Here, the one-sentence takeaway is enough: a stronger base currency makes that country's exports more expensive abroad.
Calculating the Percentage Change in a Currency
The percentage change in a currency uses the same logic as any percentage-change calculation, applied carefully to a defined quote.
Where:
= old quote, price currency per unit of base currency
= new quote, price currency per unit of base currency
A positive result means the base currency appreciated. A negative result means the base currency depreciated. The result is always stated relative to the currency in the denominator of the original quote, so keep the units attached at every step.
[INSERT nominal-real-exchange-rates-percentage-change.png HERE] Alt text: Nominal and real exchange rate notation with currency percentage change steps.
Worked Example
Priya, a treasury analyst at a UK-based import firm, tracks the quote to plan payments to a US supplier. On January 1, the quote is = 1.20, meaning 1.20 USD buys 1 GBP. By June 1, the quote rises to = 1.26.
Step 1: Percentage change in GBP (the base currency).
The pound appreciated 5.00% against the dollar. Since GBP is the base currency and the quote rose, this matches the appreciation rule directly.
Step 2: Percentage change in USD using the reciprocal quote.
The dollar depreciated 4.76%, not 5.00%. The two percentage changes are not exact negatives of each other, even though they describe the same market move. This is the reciprocal-rate caution in action.
Step 3: Real exchange rate.
Suppose the UK price index is 108 and the US price index is 112 (both indexed to a base of 100).
Using domestic currency = USD and foreign currency = GBP, with = 1.26:
The nominal quote shows the pound gaining 5.00% against the dollar. After adjusting for relative price levels, the real rate of 1.2150 is below the nominal rate of 1.26.
UK price levels rose less than US price levels over the period, so the pound's real purchasing-power gain against the dollar is smaller than the nominal move suggests. Priya should budget using the nominal rate for the actual cash payment but use the real rate to judge whether UK goods have become genuinely more or less competitive.
Common Exam Traps
Reversing base and price currencies. Candidates read S(USD/EUR) and assume EUR is being priced in the numerator. Always identify which currency is the single unit (base) before calculating anything.
Using the new rate in the denominator. The percentage-change formula requires the old quote (S0) in the denominator. Placing S1 there inflates or shrinks the result and produces a wrong answer.
Interpreting a higher price-per-base quote as base depreciation. A rising S(P/B) always means the base currency strengthened. This is one of the most common sign errors on exam calculations.
Claiming reciprocal percentage changes are exact negatives. As shown in the worked example, a 5.00% base-currency appreciation does not equal a 5.00% price-currency depreciation. The two calculations use different denominators.
Using a real-rate formula without defining domestic and foreign price levels. Plugging numbers into without confirming which price index belongs in the numerator produces a real rate with the wrong direction of adjustment.
Practice Question
On March 1, the spot exchange rate is = 0.92, meaning 0.92 Canadian dollars buys 1 Australian dollar. On September 1, the quote changes to = 0.97. Which of the following correctly states the percentage change in the Australian dollar and the resulting currency movement?
The Australian dollar appreciated approximately 5.43%, and the Canadian dollar depreciated.
The Australian dollar depreciated approximately 5.43%, and the Canadian dollar appreciated.
The Australian dollar appreciated approximately 5.00%, and the Canadian dollar appreciated.
Correct Answer: A
Percentage change in the base currency , or 5.43%. Since AUD is the base currency and the quote rose, AUD appreciated. Because CAD is the price currency in this quote, CAD depreciated.
Option B. reverses the direction: it treats a rising as AUD depreciation, the classic sign-reversal trap.
Option C. uses the wrong denominator in the calculation (0.05/1.00 style rounding) and incorrectly claims both currencies appreciated at once, which is not possible for a single currency pair.
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FAQs About Nominal vs Real Exchange Rates
What is the difference between a nominal and real exchange rate?
The nominal exchange rate is the quoted market rate between two currencies with no adjustment. The real exchange rate adjusts that quote for relative price levels in the two countries, showing the change in purchasing power rather than just the price of the currency.
How do you calculate a currency's percentage change?
Use , applied to a clearly defined quote with the base currency identified. The result describes the percentage change in the base currency, not automatically the price currency.