# Exchange Rates

The term exchange rate refers to the price of one currency in relation to another currency. For example, the exchange rate between the Chinese Yuan (CNY) and the South African Rand (ZAR) is 1.93. This means that the base currency, the Chinese Yuan, can buy 1.93 units of the South African Rand. That is:

$$\frac{\text{South African Rand (ZAR)}}{\text{Chinese Yuan (CNY)}} = \frac{1.93}{1} = \frac{\text{A}}{\text{B}} = \frac{\text{Price Currency}}{\text{Base Currency}}$$

Note: The base currency is always set equal to one and is always shown in the denominator.

The exchange rate can be defined as the number of units of one currency (price currency) that one unit of another currency (base currency) will buy. The exchange market is the world’s largest market, where all forms of exchange transactions are carried out.

## Base Currency

For example, the ZAR/CNY exchange rate of 1.6459 implies that 1 Chinese Yuan will buy 1.6459 South African Rand. Therefore, the Chinese Yuan is the base currency, and the South African rand is the price currency in this case.

A decrease in the exchange rate will mean that the base currency depreciates while the price currency appreciates. Hence, the base currency (Chinese Yuan) can only buy less of the price currency (South African Rand) than it would do before the exchange rate declines. This type of exchange rate is called a nominal exchange rate.

## Real Exchange Rates

The number of units of domestic currency per unit of foreign currency is known as the spot exchange rate. It is used to determine the foreign price level in the domestic currency. We can define the spot exchange rate mathematically as the foreign price level in domestic currency divided by foreign price levels:

$$S_{d/f} =\frac{\text{Foreign price level in domestic currency}}{ P_f }$$

$$\Rightarrow \text{The foreign price level in domestic currency}=S_{d/f}\times P_f$$

Where:

$$S_{d/f}$$ = Spot exchange rate

$$P_f$$ = Foreign price levels

Now, define $$P_d$$ as the domestic price level. Then, the ratio between the foreign and domestic price levels is the real exchange rate. That is:

$$\text{Real exchange rate}=\frac{S_{d/f }\times P_f}{P_d} =S_{d/f}\times \frac{P_f}{P_d}$$

## Forward Exchange Rates

Forward exchange rates refer to the cost at which one currency can be traded for another currency in a future transaction. There is a  distinction between spot transactions (involving spot exchange rates) and forward transactions (involving forward exchange rates). While a spot exchange rate involves an exchange of currency for immediate delivery, forward rates are agreements to exchange currencies at a future date and at a price agreed upon today.

## Question

A USD/CAD currency rate of 1.6598 most likely implies that:

Solution

The base currency, which is the Canadian Dollar (CAD), can buy 1.6598 units of the price currency (USD).

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