Chapter 1

Foreign Exchange

Copyright © 2004 Pearson Addison-Wesley. All rights reserved. 1-2

Introduction

• In this chapter we cover:

– foreign exchange quotes

– relationship between different types of quotes

– nature of bid-ask spreads in the foreign exchange market

– the implications of no-arbitrage conditions

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Direct Exchange Quotes

• A direct exchange rate is the domestic price of foreign currency.

• Let “DC” be the domestic currency, and “FC” be the foreign currency.

• A direct quote could be represented as:0.5 DC : 1 FC, for example.

Copyright © 2004 Pearson Addison-Wesley. All rights reserved. 1-4

More on Direct Quotes

• For example, the Japanese quote the U.S. dollar exchange rate as 150 Yen/$ (150 yen per dollar) — a direct rate in Japan.

• Quotations are usually given with five digits. For example,

• 150.51 Yen/$• 0.6079 pounds sterling/$

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Indirect Foreign Exchange Quotes

• An indirect exchange rate is the amount of foreign currency equivalent to one unit of domestic currency.

• For example, 2 FC: 1 DC– Note this conveys the same information as

our previous example.– Another example: 0.0067$/Yen would be

an indirect quote in Japan.

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Quote Conventions • It is important to remember that in countries

other than in the United States, all exchange rates with the dollar are usually given as direct rates.

• There are two exceptions that give the indirect rates in countries other than the United States:– British pound (has always been quoted as dollar

price of one pound).– Euro (convention adopted quotes the foreign

currency value of one euro).

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Quote Conventions (Continued)

• American terms: when quotations involve the U.S dollar, the dollar price of one unit of the second currency — a direct quote from the U.S. perspective.

• European terms: the amount of the second currency per U.S dollar, an indirect quote from the U.S perspective.

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Quotation Conventions (page 5)

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Bid-Ask Quotes

• Bid price: the exchange rate at which the dealer is willing to buy a currency.

• Ask (offer) price: the exchange rate at which the dealer is willing to sell a currency.

• Midpoint price = (ask + bid)/2

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Bid-Ask Quotes

• Consider the following direct quote in the United States:

($/Euro) 0.9838 – 0.9841

• The bid price is 0.9838 $/Euro

• The ask price is 0.9841 $/Euro

• The midpoint price is 0.98395 $/Euro

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Bid-Ask (Offer) Quotes and Spreads (page 5)

• Note:– The DC/FC direct ask exchange rate is the

reciprocal of the indirect bid exchange rate.– The DC/FC direct bid exchange rate is the

reciprocal of the indirect ask exchange rate.

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Bid-Ask Spread

• Difference between bid and ask price.

• Can also be calculated as a percentage:

Bid-ask spread = 100*(ask – bid)/ask

• Size of bid-ask spread increases with exchange rate uncertainty (volatility) because of the bank/dealer risk aversion.

• Spreads are larger for currencies that have a low trading volume (thinly traded currencies).

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Arbitrage

• Arbitrage involves the simultaneous purchase of an undervalued asset or portfolio and sale of an overvalued but equivalent asset or portfolio, in order to obtain a risk free profit on the price differential.

• Arbitrage keeps exchange rates in line with each other and with risk free interest rates.

– For example, the $/Euro rate must be the same, at a given instant, in Frankfurt, Paris and New York.

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Cross Rates

• A cross rate is the exchange rate between two countries inferred from each country’s exchange rate with a third country.

• For example, bank A gives the following quotations:• Euro/$ = 0.9000 – 0.90020• Yen/$ = 121.00 – 121.02– Calculate the yen/euro rate:

• Yen/Euro bid rate = 121.00/0.90020 = 134.41• Yen/Euro ask rate = 121.02/0.9000 = 134.47• The resulting quotation is: Yen/Euro = 134.41 – 134.47

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Two types of arbitrage opportunities to consider...• With respect to the exchange rate between

two countries, the bid-ask spread in one country should be aligned with the bid-ask spread in the other. If not, a bilateral arbitrage opportunity exists.

• A triangular arbitrage opportunity occurs if the quoted cross-rate between two currencies is higher or lower than the cross-rate implied by the exchange rates of the two currencies against a third currency.

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Triangular Arbitrage

• Triangular arbitrage involves three steps:

– Pick the cross-rate currency

– Determine whether the cross-rate bid-ask quotes are in line with the direct quotes by determining whether it is cheaper to buy foreign currency directly or indirectly.

– If the actual cross-rate quote is not in line with the quoted cross-rate quotes, an arbitrage opportunity exists.

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Forward Rates

• Spot rates are quoted for immediate currency transactions (although in practice it takes place 48 hours later).

• Forward exchange rates are contracted today but with delivery and settlement in the future.

• In a forward, or futures, contract a commitment is irrevocably made on the transaction date, but delivery takes place later, on a date set in the contract.

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Forward Premiums

• Forward exchange rates are often quoted as a premium, or discount, to the spot exchange rate.

• Given an exchange rate of x/y, the annualized forward premiumon y currency equals:

[(Forward rate - Spot rate)/Spot rate]*(12/no. of months forward)*100%

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Forward Premiums

• “Strength” is defined by the existence of a premium.

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Interest Rate Parity

• The interest rate parity relationship is that the forward discount (premium) equals the interest rate differential between the two currencies.– For two currencies, A and B, with the exchange

rate quoted as the number of units of B for one unit of A,

[(Forward rate - Spot rate)/Spot rate] = (ra - rb)/(1 + ra)

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Covered Interest Rate Arbitrage

• The process of simultaneously borrowing the domestic currency, transferring it into foreign currency at the spot exchange rate, lending it, and buying a forward exchange rate contract to repatriate the foreign currency into domestic currency at a known forward exchange rate. The net result of such an arbitrage should be nil.

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Interest Rate Parity Example• Spot rate = 1.6400 $/pound sterling• 90 day Forward rate = 1.6236 $/pound

sterling• U.S. risk free rate = 1.15%• UK risk free rate = 3.75%

– Annualized forward premium = – 4.0%– Interest rate parity is violated.

• Dollar is getting stronger, pound weaker• Borrow in foreign market (£), Invest

domestically ($), buy £ forward.