The foreign exchange market

The foreign exchange market is the electronic trading of foreign currencies between commercial banks, dealers, and businesses. Generally, the foreign exchange markets have no central marketplace, and participants trade via sophisticated communications systems.

The following is a typical classification of the participants in the foreign exchange market:

1. Arbitrageurs: Arbitrageurs seek to earn risk-free profits by taking advantage of differences in exchange rates among countries. They buy currencies that are underpriced at one center and simultaneously sell the same set of currencies at the centers where they are overpriced, thereby locking in a risk-free arbitrage profit.
2. Hedgers: Multinational firms have their operations in a number of countries and their assets and liabilities are designated in foreign currencies. The foreign exchange rates fluctuations can cause diminution in the home currency value of their assets and liabilities. They operate in the foreign exchange market as hedgers to protect themselves against the risk of fluctuations in the foreign exchange rates.
3. Speculators: Speculators are guided by purely profit motive. They trade in foreign currencies to benefit from the exchange rate fluctuations. They take risks in the hope of making profits.

What is Exchange Rate?

An exchange rate specifies the number of units of a given currency that can be purchased with one unit of another currency. An exchange rate can either be direct or indirect.

A direct quote is the number of units of a local/domestic currency that exchanges for one unit of a foreign currency. A direct quote between the Japanese yen and USD will be stated as follows:

JP¥ 112/USD or 112 ¥/USD

This means that JP¥ 112 is required to buy 1 USD.

An indirect quote is the number of units of a foreign currency that can be exchanged for one unit of local currency. An indirect quote between Japanese yen and USS will be stated as follows: USD 0.0090.

    \[    Indirect\quad quote =\frac{1}{Direct\quad quote} \]

Thus, each one is the reciprocal of the other.

Bid-Ask Spread

Rather than charge a commission on foreign currency transactions, banks make their profits off the bid-ask spread. The bid price is the price a dealer is willing to pay to buy a currency. If you are selling the currency, you will receive this price. The ask price is the price a dealer is willing to take to sell a currency. If you are buying the currency, you will pay the ask price.

Assume the following quotes:

– A bid of 1.6625 USD/£
– An ask of 1.6635 USD/£

For the direct U.S. quote, the percentage spread (based on the ask price) is:
(1.6635 – 1.6625)/1.6635 = 0.06%

To convert a quote with bid/ask spread to a quote as viewed from the foreign country:

– The reciprocal of the direct bid becomes the indirect ask
– The reciprocal of the direct ask becomes the indirect bid

Example: If the bid is 1.8709 USD to £1 and the ask is 1.8841 USD to £1, it is possible to determine the bid-ask spread in European terms. The bid-ask spread in European terms is foreign currency pr dollar; so you are being asked to convert the bid-ask spread to £/USD. Just take the reciprocal of each number and reverse the bid-ask spread.

    \[ \frac{1}{1.8709} = 0.5345\quad and \]

    \[ \frac{1}{1.8841} = 0.53076 \]

The bid-ask spread is now 0.5308 – 0.5345

Cross rate

The cross rate is an implicit exchange rate between currencies X and Y, based on the explicit exchange rate between currencies X and Z and currencies Y and Z. For example, if the spot exchange rate between the British pound and the U.S. dollar is 0.7775/USD, and the spot exchange rate between the Canadian dollar and the British pound is 1.8325 CAD/£, the USD/CAD exchange rate can be calculated thus:

£/USD exchange rate = 0.7775 or

    \[ \frac{1}{0.7775} \]

CAD/£ exchange rate = 1.8325 or

    \[ British Pound/CAD = \frac{1}{0.7775} \]

The needed rate is USD/CAD. Thus, it will be:

    \[ \frac{USD}{CAD} = \frac{USD}{British Pound} x \frac{British Pound}{CAD} = \frac{1}{0.7775} x \frac{1}{1.8325} \]

Triangular Arbitrage

This is a round-trip sequence of three currency transactions at exchange rates that yield an arbitrage profit. It arises when cross-rates are quoted out of alignment. For example, considering the following quotes:
Currency A/Currency B – 8.25A/B
Currency C/Currency B – 1.65C/B

What should be the cross-rate for CurrencyA/Currency C (A/C) so that no arbitrage opportunities exist?

The following relationship must hold if arbitrage is to be avoided:
(A/B) (B/C) (C/A) = 1
A/B = 8.25
B/C = 1/1.65

    \[ 8.25 * \frac{1}{1.65} x Unknown = 1 \]

Therefore, A/C = \frac{1}{C/A} = \frac{1}{1/5} = 5 \]