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101 Concepts for the Level I Exam

Concept 35: Currency Cross-Rates


Cross rate is the exchange rate between two currencies derived from their exchange rate with a common third currency.

Consider the following exchange rates:

Spot rate Expected spot rate
USD/EUR 1.3690 1.3457
CHF/USD 0.9164 0.9020
USD/GBP 1.5160 1.5100

Determine the following:

  1. CHF/EUR cross rates.
  2. GBP/EUR cross rates.
  3. CHF/GBP cross rates.
  4. Does EUR appreciate/depreciate against CHF and by how much.
  5. The strongest currency over the next year.

 

Solution:

1.Spot rate:

CHF/EUR=CHF/USD*USD/EUR=0.9164*1.3690=1.2546

Expected spot rate: CHF/EUR=CHF/USD*USD/EUR=0.9020*1.3457=1.2138

2.Spot rate: GBP/EUR=GBP/USD*USD/EUR=(1/1.5160)1.3690=0.9030

Expected spot rate: GBP/EUR=GBP/USDUSD/EUR=(1/1.5100)1.3457=0.8912

3.Spot rate: CHF/GBP=CHF/USDUSD/GBP=0.9164*1.5160=1.3893

Expected spot rate: CHF/GBP=CHF/USD*USD/GBP=0.9020*1.5100=1.3620

As the quoted rate for CHF/EUR drops from 1.2546 to 1.2138, the EUR depreciates relative to CHF.

Percentage depreciation in EUR relative to CHF = (1.2138/1.2546 — 1) = -3.25\%

From the change in quoted exchange rates we can see that USD strengthens relative to both EUR and GBP.

Whereas USD depreciates relative to CHF.

Hence, the strongest currency is CHF.