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

1-3 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, Yen/$ pounds sterling/$

1-5 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: $/Yen would be an indirect quote in Japan.

1-6 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).

1-7 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.

1-8 Quotation Conventions (page 5)

1-9 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

1-10 Bid-Ask Quotes Consider the following direct quote in the United States: ($/Euro) – The bid price is $/Euro The ask price is $/Euro The midpoint price is $/Euro

1-11 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.

1-12 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).

1-13 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.

1-14 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/$ = – Yen/$ = – –Calculate the yen/euro rate: Yen/Euro bid rate = / = Yen/Euro ask rate = / = The resulting quotation is: Yen/Euro = –

1-15 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.

1-16 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.

1-17 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.

1-18 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 premium on y currency equals: [(Forward rate - Spot rate)/Spot rate]*(12/no. of months forward)*100%

1-19 Forward Premiums “Strength” is defined by the existence of a premium.

1-20 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] = (r a - r b )/(1 + r a )

1-21 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.

1-22 Interest Rate Parity Example Spot rate = $/pound sterling 90 day Forward rate = $/pound sterling U.S. risk free rate = 1.15% UK risk free rate = 3.75% –Annualized forward premium = – 4.0% –Interest rate parity is violated. Dollar is getting stronger, pound weaker Borrow in foreign market (£), Invest domestically ($), buy £ forward.