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# Percentage Change in a Currency Relative to Another Currency

## Calculating Percentage Appreciation/Depreciation

To calculate the percentage change, one needs to clearly understand the base currency and the price currency.  Let’s take the Chinese Yuan (CNY) and South African Rand (ZAR) example. The ZAR/CNY exchange rate increased from 1.6459 to 1.8356. Therefore, the percentage appreciation will be:

$$\frac{1.8356}{1.6459} – 1 = 11.5256\%$$

This represents an 11.5256 percent appreciation in the Chinese Yuan against the South African Rand. The ZAR/CNY exchange rate is expressed with the Chinese Yuan as the base currency and South African Rand as the price currency. In other words, you now need more South African Rands to buy one Chinese Yuan.

## Interpretation of the Percentage Appreciation/Depreciation

The appreciation of the Chinese Yuan against the South African Rand can also be expressed as a depreciation of the South African Rand against the Chinese Yuan. However, the depreciation percentage, in this case, will not be equal to the previous appreciation percentage of 11.5256%.

To invert a currency exchange rate, we have to divide 1 by the exchange rate:

If $$\frac{ZAR}{CNY} = 1.6459$$

Then,
$$\frac{CNY}{ZAR} = \frac{1}{1.6459} = 0.6076$$

To calculate the depreciation percentage of South African Rand if the exchange rate ZAR/CNY increased from 1.6459 to 1.8356, we have to invert the exchange rate from ZAR/CNY to CNY/ZAR so that the Chinese Yuan becomes the price currency and the South African Rand, the base currency. That is:

$$\frac{\frac{1}{1.8356}}{\frac{1}{1.6459}} – 1 = \frac{0.5448}{0.6076} -1 = -10.3358\%$$

Thus, we can see that the depreciation percentage of the South African Rand is not the same as the Chinese Yuan’s appreciation.

### Example: Appreciation/Depreciation With a Forward Rate

A forex trader noticed that the USD/EUR spot rate is 1.2960 and is expected to be 1.2863 after one year (forward rate). Calculate the euro (EUR) expected appreciation/depreciation against the US dollar over the next year.

##### Solution

We know that we are dealing with USD/EUR quotes. So, we calculate as:

$$\frac{1.2863}{1.2960}-1=-0.00748=-0.748\%$$

This was expected because clearly, there was a decrease in USD/EUR, indicating that EUR is depreciating.

## Question

Which of the following best describes a 4% appreciation in the ZAR/CNY exchange rate?

A. This represents a 4 percent appreciation in the South African Rand (ZAR) as compared to the Chinese Yuan.

B. This represents a 4 percent appreciation in the Chinese Yuan (CNY) as compared to the South African Rand.

C. This represents a 4 percent depreciation in the Chinese Yuan (CNY) as compared to the South African Rand.

Solution

The correct answer is B.

A 4% appreciation in the ZAR/CNY exchange rate  represents an appreciation of the base currency against the price currency. In this case, the Chinese Yuan appreciates against the South African Rand. Therefore, the appreciation represents a 4 percent increase in Chinese Yuan, relative to the South African Rand.

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