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# Understanding The Mechanics of Exchange Rates

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An exchange rate is a measure of how much of one currency may be exchanged for another currency. These rates may be in the form of either direct or indirect quotes made by a foreign currency trader who is usually employed by a  large commercial bank. Denominating a transaction in a currency other than the entity’s domestic currency requires the establishment of a rate of exchange between the currencies. The international monetary system establishes rates of exchanges between currencies through the use of a variety of systems. The selection of a particular monetary system and the resulting exchange rates have a significant effect on international business and the risk associated with such business.

Through this post I would Introduce and define the various terms associated with exchange rates, including spot rates, forward rates, premiums, and discounts. A Must know mechanic jargons for one who wants to learn about exchange rates. Enjoy!

### Change Relative to Another Currency

A direct quote measures how much of the domestic currency must be exchanged to receive one unit of the foreign currency (1 FC). Direct quotes allow the party using the quote to understand the price of the foreign currency in terms of its own “base” or “domestic currency“. This method is frequently used in the United States, and direct quotes are published daily in financial papers such as The Wall Street Journal.

Indirect quotes“, also known as European terms, measure how many units of foreign currency will be  received for one unit of the domestic currency. Thus, if the direct quote for a “foreign currency (FC)” is \$0.25, then one FC would cost \$0.25. The indirect quote would be the reciprocal of the direct quote, or 4 FC per dollar (\$1.00 divided by \$0.25).

Exchange Rate Quotes
Direct Quote: 1 FC = \$0.25
Indirect Quote: \$1 = 4 FC

Foreign  currency  exchange  rate  quotes  are  reported  in The Wall  Street  Journal and  are  also available on selected Web sites. Using Canada as an example, as of November 1, 2009, the direct quote is \$0.6507, and the indirect quote is \$1 = 1.5367 Canadian dollars.

The business news often reports that a currency has strengthened (gained) or weakened (lost) relative to another currency. Assuming a “direct quote system“, such changes measure the difference between the new rate and the old rate, as a percentage of the old rate. For example: if the dollar strengthened or gained 20% against a foreign currency (FC)  from  its previous rate of \$0.25, the dollar would now command more FC  (i.e.,  the FC would be cheaper  to buy). To be exact, the new exchange rate would be \$0.20 [\$0.25 – (20% x 0.25)]. Therefore, the strengthening currency would  be  evidenced  by  a  reduction  in  the  directly  quoted  amount  and  an  increase  in  the  indirectly quoted amount.

The opposite would be true for a weakening of the domestic currency. The reaction to a strengthening or weakening of a currency depends on what type of transaction is contemplated. For example: an American exporter would want  a weaker dollar because  the  foreign importer would need fewer of its currency units to acquire a dollar’s worth of U.S. goods. Thus, U.S. goods would cost less in terms of the foreign currency. If the dollar strengthened so that one could acquire more foreign currency units  for a dollar,  importers would benefit. Therefore, U.S. companies and citizens would have to spend fewer U.S. dollars to buy the imported goods.

Exchange rates often are quoted in terms of a buying rate (the bid price) and a selling rate (the offered price)“. The buying and selling rates represent what the currency broker (normally a large commercial bank) is willing to pay to acquire or sell a currency. The difference or spread between these two rates represents the broker’s commission and is often referred to as the points. The spread is  influenced by  several  factors,  including  the  supply of and demand  for  the currency,  the number of transactions taking place, currency risk, and the overall volatility of the market.

Example:

Assume a currency broker agrees to pay \$0.20 to a holder of a foreign currency and agrees to sell that currency  to a buyer of  foreign currency  for \$0.22. In this case,  the broker will receive a commission of \$0.02 (\$0.22 – \$0.20). In the United States, rates generally are quoted between the U.S. dollar and a foreign currency. However, rates between two foreign  currencies  are  also quoted and are referred to as cross rates.

### Types of Exchange Rates

Exchange rates fall into two primary groups. A spot rate is the rate of exchange for a currency with delivery, selling, or buying of the currency normally occurring within two business days. In addition  to  exchange  rates governing  the  immediate delivery of  currency,  forward  rates apply to the exchange of different currencies at a future point in time, such as in 30 or 180 days. Although not all currencies are quoted in forward rates, virtually all major trading nations have forward rates.

An agreement to exchange currencies at a specified price with delivery at a specified  future point in time is a forward contract. As more fully discussed  in the derivatives module, a forward contract is a derivative instrument whose underlying is a foreign currency exchange rate. Forward exchange contracts may be held as an investment or held as part of a strategy to reduce or hedge against exchange rate risk associated with another transaction.

A forward contract, used to hedge against the risk associated with changing exchange rates, specifies the future exchange date and the forward rate of exchange. Although future exchange dates typically are quoted in 30-day intervals, contracts can be written to cover any number of days. To illustrate a forward contract, assume the forward  rate  to buy a FC  to be delivered  in 90 days  is \$1.650. This means that, after  the  specified time from the inception of the contract date (90 days), one FC will be exchanged for \$1.650, regardless of what the spot rate is at that time.
Several aspects of spot rates and forward rates are noteworthy:

• First, typically both rates are constantly changing. Spot rates are revised daily; as they change, forward rates for the remaining time covered by a given forward contract also change even though the forward rate at inception is fixed. When  there  is no more  remaining  time,  the current  forward  rate becomes  the  spot  rate. Therefore, the value of a forward contract changes over the forward period. For instance: in the above example, if the forward rate is 1 FC = \$1.652 with 30 days remaining, the right to buy FC at the original fixed forward rate of 1 FC = \$1.650 suggests that the value of the forward contract has increased. Rather than paying a forward rate of \$1.652 to acquire FC  in 30 days,  the holder of the original  forward contract must only pay the  fixed rate of \$1.650.
• Second, the ultimate value of the forward contract must be assessed by comparing the fixed forward rate against the spot rate at the settlement date. In the above example, at the settlement date, the holder of the contract will pay the fixed rate of 1 FC = \$1.650 to buy an FC rather than the spot rate of 1 FC = \$1.655. The total change in value is represented by the difference between the original fixed forward rate and the spot rate at settlement date.
• Finally, the difference between a forward rate and a spot rate represents a premium or discount which is traceable to a number of factors. This difference between the spot and forward rate represents the time value of the forward contract.  If the forward rate is greater than the spot rate at inception of the contract, the contract is said to be at a premium (as in the above example). The opposite situation results in a discount. Quoting premiums or discounts (known as forward differentials), rather than forward rates, is common industry practice.

### Forward Rates Employ a Forward Exchange Contract

Forward Rate > Spot Rate
(At inception of contract)

At a Discount
Forward Rate < Spot Rate
(At inception of contract)

At inception, the difference between the forward and spot rates represents a contract expense or income to the purchaser of the forward contract. A number of factors influence forward rates and, thus, account  for  the difference between a  forward rate and a spot rate.

A primary factor is the interest rate differential between holding an investment in foreign currency and holding an investment in domestic currency over a period of  time.  It is for this reason that the difference between a forward rate is referred to as the time value of the forward contract. For example: if a broker sold a contract to deliver foreign currency in 30 days, the interest differential would be the difference between:

• The interest earned on investing foreign currency for the 30 days prior to delivery date and
• The 30 days of interest lost on the domestic currency  that was not  invested but was used  to acquire the foreign currency needed for delivery.

Assume that the spot rate is 1 FC = \$0.60 and that you want  to determine a 6-month  forward rate. Further, assume that the dollar could be invested at 4.5% and the FC could be invested at 7.25%. The forward rate would be calculated as follows:
U.S. Dollars    Foreign Currency(FC)
Value today  . . . . .         \$600.00          1,000 FC
Interest rate . . . .           4.5%                7.25%
Six months of interest   \$13.50            36.25 FC
Value in six months      \$613.50          1036.25 FC

6-month forward rate = \$613.50 / 1036.25 FC = 1 FC = \$0.592

The forward rate for a currency can also be derived by the following formula:

Forward rate = Direct spot rate at the beginning of period t x [1 – Interest rate for domestic investment during period t] / [1 – Interest rate for foreign country investment during period t]

Using the formula to solve the previous example results in the following, based on 6-month interest rates:

Forward rate of \$0.592 = \$0.60 x [(1 + 0.0225)/(1 + 0.03625)]

If the interest yield on the FC is greater than the yield on the U.S. dollar, the forward rate will be less than the spot rate (contract sells at a discount). The forward contract will sell at a premium if the opposite is true. The forward rate based on interest differentials will be slightly different than the quoted forward rate because the quoted rate includes a commission to the foreign currency broker.

Furthermore, other factors in addition to interest differentials could be incorporated into the forward rate. These other  factors  include  the volatility of  the  spot  rates,  the  time period covered by the contract, expectations of future exchange rate changes, and the political and economic environments of a given country.

As previously mentioned, changes in exchange rates represent an additional business risk when transactions are denominated in a foreign currency. The accounting  for  foreign  currency  transactions measures  this  risk  and  demonstrates  the  use  of  both spot and forward rates. The current international monetary system is a floating system in which rates of exchange between currencies change in response to a variety of factors including trade balances, interest rates, money supply, and other economic factors. Spot rates represent the current rate of exchange between two currencies. A forward rate represents a future rate of exchange at a future point in time. If the forward rate exceeds the spot rate, the contract is at a premium rather than a discount.

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