# Exchange Rates

A foreign exchange rate is the rate at which one currency can be exchanged with another. A foreign exchange rate has two components: a bid rate, the rate which the foreign currency can be sold and an ask rate, the rate at which the foreign currency can be purchased. The difference between the two rates is called the bid-ask spread.

The current USD/JPY quote is 108.6900 – 108.7100 in US. In this exchange rate, USD is the base currency, the currency for which exchange rate is quoted and JPY is the price currency, i.e. the currency used to price the USD. There are two rates, the rate to the left is the bid rate and the rate to the right is the ask rate (also called offer rate). What it means is that you can sell a USD to the dealer at the exchange rate of 108.6900 yens and purchase a USD for 108.7100 yens. The ask rate is always higher than the bid rate this is because a dealer will always want to sell at a higher rate. The difference is called the bid-ask spread and it represents the profit of the dealer.

## Foreign exchange quotes

There are three ways in which foreign exchange rates are quoted: (a) direct quote, (b) indirect quote and (c) cross rate.

Direct quote is the foreign exchange rate quoted with the domestic currency in the denominator. It is called direct quote because it can be used to determine the units of domestic currency needed to buy or sell a foreign currency.

Indirect quote is the foreign exchange rate quoted with the foreign currency in the denominator. It is the inverse of the direct quote. A direct quote can be converted to an indirect quote using the following formula:

$$\text{JPY}/\text{USD quote}\ =\frac{\text{1}}{\text{USD}/\text{JPY quote}}$$

Cross rate is the foreign exchange rate for currency A and B worked out using two quotes for currency A and C and C and B. Cross rates can be determined using the following formula:

$$\text{Cross Rate for A}/\text{B}=\frac{\text{A}}{\text{C}}\times\frac{\text{C}}{\text{B}}$$

### Example: direct vs indirect quote

The USD/JPY rate quoted above (108.6900 – 108.7100) is the direct quote in a Japanese market because the JPY is in the price currency.

Let’s find the reciprocal of the USD/JPY quote above. The reciprocal of the bid rate and ask rate above works out to 0.009200 and 0.009198 respectively. The JPY/USD exchange rate will be 0.009198-0.009200. Please notice that we have switched the positions of the quotes i.e. the original direct quoted bid rate is the indirect quote ask rate and original direct quoted ask rate is the indirect quote bid rate. This is because the ask rate must always be higher than the bid rate.

## Spot exchange rate vs forward exchange rate

Spot exchange rate is the rate that applies to immediate exchange of currencies while the forward exchange rate is the rate determined today at which two currencies can be exchanged at some future date.

There are two models used to forecast exchange rates: purchasing power parity and interest rate parity.

Under the purchasing power parity condition, it is expected that the currency exchange rates which adjust between two markets such that the ultimate purchasing power of both currencies will remain the same. There are two version of purchasing power parity: absolute purchasing power parity and relative purchasing power parity. Following is the equation for forward exchange rate based on relative purchasing power parity:

$$\text{f}=\text{S} _ \text{0}\times\left(\frac{\text{1}+\text{i} _ \text{d}}{\text{1}+\text{i} _ \text{f}}\right)^\text{t}$$

Where f and S0 are the forward exchange rate and spot exchange rate quoted with the domestic currency as the price currency, id and if are the inflation rates in domestic country and foreign country respectively and t is the time period involved.

### Interest rate parity

The interest rate parity attempts to forecast exchange rate based on the difference between the risk-free interest rates in two markets. The premise is that the currency of the country which offers higher interest rate should appreciate because there will be higher demand for that currency. Following is the formula that can be used to work out forward exchange rate using interest rate parity relationship:

$$\text{f}=\text{S} _ \text{0}\times\left(\frac{\text{1}+\text{r} _ \text{d}}{\text{1}+\text{r} _ \text{f}}\right)^\text{t}$$

Where f and S0 are the forward exchange rate and spot exchange rate (direct quote), rd and rf are the risk-free interest rates in domestic country and foreign country respectively and t is the time period.

## Foreign exchange risk management

There are three ways in which a company can be exposed to foreign exchange risk: (a) transaction exposure, (b) translation exposure and (c) economic exposure. Transaction exposure arises from the possibility of exchange rate movement between the date on which an asset or liability arises and the date on which it is settled. Translation exposure arise when a foreign company financial statements are translated from its functional currency to the reporting currency for consolidation purpose. Economic exposure represents the effect of exchange rate on a company’s business.

The transaction exposure can be management using either (a) forward contracts and futures contracts, (b) money market hedge, (c) currency options and (d) currency swaps.

The translation exposure can be managed using the balance sheet hedge.