Currency quotes: USD/EUR up 4% means the dollar fell 3.85%
USD/EUR moves from 1.2500 to 1.3000. A candidate who reads that as a 4.00% depreciation of the dollar has the sign right and the number wrong: the euro appreciated 4.00%, but the dollar depreciated 3.85%, because each percentage is measured against a different starting value.
Which currency the quote is pricing
In the convention used throughout CFA economics, a quote is written as price currency / base currency. The base currency is the one being priced, and it is always one unit. The price currency is what that one unit costs.
USD/EUR = 1.2500 means one euro costs 1.2500 dollars
So the euro is the base, the dollar is the price currency, and the number on the page is a price of euros. That reading is the whole exercise. Get it backwards and every subsequent step inherits the error, including steps that are themselves done correctly.
The slash is not division and it is not a hint. Market desks write the same pair as EURUSD, financial media often writes it as EUR/USD, and neither matches the CFA ordering. A question that says "the USD/EUR rate" has told you which currency is being priced, and it is the one after the slash.
A rising quote means the base currency got stronger
When USD/EUR rises from 1.2500 to 1.3000, a euro now costs more dollars than it did. The euro appreciated. The dollar, being the thing you now need more of, depreciated.
The trap is that "the USD/EUR rate went up" sounds like a statement about the dollar, because the dollar is written first. It is not. It is a statement about the price of the base currency, and the base currency is the euro.
One sanity check settles it in a few seconds: pick a real amount. At 1.2500, 10,000 euros buy 12,500 dollars. At 1.3000 the same 10,000 euros buy 13,000 dollars. The euro got more valuable. No notation reasoning required.
Why 4.00% and 3.85% are both right
The appreciation of the base currency is read straight off the quote.
EUR appreciation = 1.3000 / 1.2500 − 1 = 4.00%
The depreciation of the price currency needs the inverted quote, because the dollar's value in euros is a different series with a different starting point.
EUR/USD before = 1 / 1.2500 = 0.8000
EUR/USD after = 1 / 1.3000 = 0.7692
USD depreciation = 0.7692 / 0.8000 − 1 = −3.85%
Simply flipping the sign on 4.00% gives −4.00%, which is the distractor. The shortcut that does work is 1 / 1.04 − 1 = −3.85%, and it works because appreciation and depreciation are reciprocals, not negatives of each other.
The amount check again: 10,000 dollars bought 8,000 euros at the old rate and buys 7,692.31 euros at the new one. That is 307.69 euros gone, which is 3.85% of 8,000. The dollar's loss is smaller in percentage terms because it is measured against the larger base.
The gap widens with the size of the move. A 4% appreciation pairs with a 3.85% depreciation, but a 25% appreciation pairs with a 20% depreciation, and a doubling of the quote pairs with a 50% loss. On exam-sized moves the two numbers sit close enough together that both appear among the answer choices.
Direct and indirect add a second layer
Direct and indirect describe the same quote from a location, not from the page. A quote is direct when the price currency is the domestic currency, and indirect when the domestic currency is the base.
USD/EUR is a direct quote to a US investor and an indirect quote to a European one. The rate has not changed. Only the person reading it has. Questions that specify the investor's home country are usually doing it to make this distinction load-bearing rather than as background colour.
Quick reference
| Question wording | What it establishes | Risk if missed |
|---|---|---|
| USD/EUR | EUR is the base, priced in USD | Reading the first currency as the one being priced |
| The quote rises | Base currency appreciated | Concluding the first-written currency strengthened |
| Appreciation of the base | New rate / old rate − 1 | Inverting the quote when no inversion is needed |
| Depreciation of the price currency | Invert both rates, then compute | Flipping the sign on the appreciation figure |
| Direct quote | Domestic currency is the price currency | Ignoring which country the investor is in |
Both numbers in this trap are correct answers to questions that differ by one word. "By how much did the euro appreciate" and "by how much did the dollar depreciate" describe the same market move, and they do not share an answer. Reading the quote out loud as "one euro costs 1.2500 dollars" resolves the direction; inverting before computing resolves the size.
The same discipline shows up in the cash conversion cycle, where one term enters the sum with the opposite sign to the other two: in both cases the arithmetic is trivial once the direction has been pinned down, and wrong every time it has not.
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