Université Paris-Nord

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1 Université Paris-Nord Théorie des choix de portefeuilles internationaux Master 1 «Economie et Finance internationales» Jean-Michel Courtault 1-1

2 " -C'est pas très bon, hein? -C'est même très mauvais! -Eh, oui! Maintenant je suis seulement le gérant et toute la journée je sers de la merde. -Mais au Relais des Cigales s'en était déjà. -Oui, peut-être. Oui, mais c'était moi qui la faisait." (L'aile ou la cuisse, Claude Zidi) 1-2

3 Organisation du cours CM : Jean-Michel Courtault TD: Abdelli Hanen et Jean-Michel Courtault s: abdellihanen@yahoo.fr courtault.jean-michel@univ-paris13.fr Contrôle des connaissances TD: 50% Partiel: 50% 1-3

4 Bibliographie Ouvrage de référence: Bruno Solnik et Dennis McLeavy, Global Investment, Pearson, 6 ème édition,

5 Chapter 1 Currency Exchange Rates

6 Text Outline Chapters 1-3 set out the foundation of exchange rates. Chapters 4-8 explore the various assets available for international investing. Chapters 9-13 develop the techniques and perspective of global investment and portfolio management. 1-6

7 Chapter One - Outline In this chapter we cover: currency exchange rate quotations (direct and indirect; spot and forward) cross-rate calculations nature of bid-ask quotes and spreads calculation of forward premiums/discounts on exchange rates. covered interest rate parity covered interest arbitrage 1-7

8 Currency Abbreviations Abbreviations are used to refer to the various currencies. These abbreviations could be commonly used symbols or official three-letter codes. Financial newspapers such as the Financial Times generally use symbols, while traders use three-letter codes. Symbols include $ (U.S. dollar), ( Japanese yen), (euro), (British pound), A$ (Australian dollar), and Sfr (Swiss franc). Three-letter codes for the same currencies are USD, JPY, EUR, GBP, AUD, and CHF. We will alternatively use in this book (as done in the real world) the various currency abbreviations that are commonly encountered. For example, the Japanese yen can be referred to as, JPY, or yen. 1-8

9 Currency Exchange Rate Quotations A currency exchange rate is the rate used to exchange two currencies. An exchange rate states the price of one currency in terms of units of another currency. Examples: $:, :$, :$ Note: the notation in this new edition of the text has changed relative to previous editions. 1-9

10 Quote Convention used in this text All quotes in this text will be presented as a:b = S where a is the quoted currency b is the currency in which the price is expressed S is the price of the quoted currency a in units of currency b For example, $: = 130 means the U.S. dollar is quoted at 130 Japanese yen ( ) per dollar. Or the U.S. dollar is priced at 130 yen. 1-10

11 Direct Exchange Quotes A direct exchange rate is the domestic price of foreign currency. For example, an American investor seeing a direct quote :$ = 1.34 knows she will pay $1.34 for one euro. To a European investor, the direct quote is $: = which says that 1 dollar (foreign currency) is worth euro. An appreciation of the foreign currency causes an increase in the direct quote. 1-11

12 Indirect Foreign Exchange Quotations An indirect exchange rate is the amount of foreign currency that one unit of domestic currency will purchase. For an American investor, the indirect quote $: = says that 1 dollar will purchase euro. Direct quotes and indirect quotes are reciprocals of each other. An appreciation of the foreign currency causes a decrease in the indirect quote. 1-12

13 Example: Direct and Indirect Exchange Rates On July 1, the British pound ( ) is quoted as :$ = Is this a direct or indirect quote from the viewpoint of an American and a British investor? A month later, the exchange rate moved to :$ = Which currencies appreciated or depreciated? 1-13

14 Example: Direct and Indirect Exchange Rates - Continued Answer: The pound is quoted in terms of dollars. This quote is a direct quote from the American viewpoint and an indirect quote from the British viewpoint. The pound is the quoted currency. Over a month, the pound s price increased from $1.80 to $1.90, so the pound appreciated and the dollar depreciated. 1-14

15 Currency Movements and Exchange Rate Quotations 1-15

16 Cross Rate Calculations 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: :$ = $: = Calculate the euro in yen ( : ) rate: ( :$) ($: ) = = The resulting quotation is: : = One euro is worth yen. 1-16

17 Cross Rate Calculations Example 2 For example, bank B gives the following quotations for the Korean won and the Brazilian real: $: won = $: R$ = Calculate the R$:won rate: ($:won) ($:R$) = / = The resulting quotation is: R$:won = One Brazilian Real is worth won. 1-17

18 Foreign Exchange Market The international currency market has two main components: A worldwide Forex market between major banks and specialized currency dealers. This is a wholesale interbank market for large transactions. It is an OTC market, by telephone and electronic trading platforms, where trading takes place 24 hours a day, 5 days a week. It is the largest and most liquid financial market in the world. A retail market where investors and corporations deal with local banks. 1-18

19 Forex Market Conventions 1 There is no need to quote both a direct and direct rate, e.g. both $: and :$. History mostly dictates the exchange rate direction that is selected: There is a decreasing order of seniority with the British pound as the senior currency. The Forex convention is to trade British pounds in units of other currencies, so the quote showing on Forex trading screens is the foreign exchange value of one GBP, that is, GBP:EUR, GBP:USD, or GBP:JPY. 1-19

20 Forex Market Conventions 1 (cont d) When the euro was introduced in 1999, it was given seniority just behind its British neighbor. Thus, the quote showing on Forex trading screens is the foreign exchange value of one euro, EUR:USD or EUR:JPY. The only exception is the British pound where the GBP:EUR is quoted. Finally, the dollar is quoted in units of all other currencies, for example, USD:JPY. 1-20

21 Forex Market Conventions 2 Not all exchange rates are traded. In a world with a large number of currencies, there are a very large number of cross exchange rates. For example, with 20 currencies, there are 380 bilateral exchange rates. The exchange rates between two minor currencies are not traded on the Forex market. Only the dollar exchange rate with each minor currency is quoted. Hence to achieve a transaction between two minor currencies, one needs to perform two transactions involving the dollar (such as between the South Korean won and Brazilian real hence our previous example with cross-rates). 1-21

22 Forex Market Conventions 2 (cont d) The obvious motivation for this rule is liquidity. At a given time, there are few transactions between two minor currencies, so it is more efficient to group all transactions against one major currency, the U.S. dollar. 1-22

23 Forex Market Conventions 3 In the Forex market, quotations on trading screens are generally given with five significant digits and three-letter codes. For example, the USD:JPY quote could appear as and the EUR:USD as Market makers quote both a bid and an ask price, and there is no additional fee or commission. 1-23

24 Bid-Ask Quotes Bid price: the exchange rate at which the dealer is willing to buy the quoted currency in exchange for the second currency. Ask (offer) price: the exchange rate at which the dealer is willing to sell the quoted currency in exchange for the second currency. The difference between the bid and ask price is called the spread. Midpoint price = (ask + bid)/2 1-24

25 Bid-Ask Quotes - Example Consider the following currency quote in the United States: $: = The bid price is $: The ask price is $: The midpoint price is $:

26 Additional terminology A pip stands for price interest point and represents the smallest price fluctuation in the currency price. It is equivalent to the tick on stock markets. E.g. :$ = The spread equals 4 pips. 1-26

27 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) and lack of liquidity because of the bank/dealer risk aversion. Spreads are larger for currencies that have a low trading volume (thinly traded currencies). 1-27

28 Two Principles for bid and ask rates The a:b ask exchange rate is the reciprocal of the b:a bid exchange rate. The a:b bid exchange rate is the reciprocal of the b:a ask exchange rate. Example: the $: quote of $: = is equivalent to a :$ quote of: :$ =

29 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 $: rate must be the same, at a given instant, in Frankfurt, Paris and New York. 1-29

30 Arbitrage Conditions with Exchange Rates An arbitrage could be created if it were profitable to buy from one bank and sell to another bank. When describing arbitrage, we are usually discussing a riskless transaction that does not require any invested capital. 1-30

31 Arbitrage Example Consider the following three banks each providing a $: quote : Bank A Bank B Bank C Does an arbitrage opportunity exist? One could buy dollars from Bank A for yen per dollar and simultaneously sell them to Bank B for yen per dollar. A small gain, but it is riskless and does not require any invested capital. 1-31

32 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. 1-32

33 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. 1-33

34 Forward Rates Spot rates are quoted for immediate currency transactions (although in practice delivery 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. 1-34

35 Forward Premiums/Discounts Forward exchange rates are often quoted as a premium, or discount, to the spot exchange rate. When a trader announces that a currency quotes at a premium, the premium should be added to the spot exchange rate to obtain the value of the forward exchange rate. If a currency quotes at a discount, the discount should be subtracted from the spot exchange rate to obtain value of the forward exchange rate. 1-35

36 Forward Premiums/Discounts Given an exchange rate of a:b, the annualized forward premium on the quoted currency a equals: Forward rate Spot Spot rate rate 12 No. months forward 100% 1-36

37 Forward Premiums/Discounts - Example If the 3 month forward exchange rate is :$ = and the spot rate is :$ = , calculate the forward premium/discount. Solution: % = 3.91% 1-37

38 Exhibit 1.1: Currency Speculation 1-38

39 Exhibit 1.2: Covered Interest Rate Arbitrage 1-39

40 Forward Quotations with Bid-Ask Spreads - Example On the Forex market, you notice the following quotes: Spot: $: = One year interest rate ($): 3 ½ 4% One year interest rate ( ): ½ - 1% What should be the quote for the one year forward exchange rate $:? 1-40

41 Forward Quotations with Bid-Ask Spreads - Example Solution: F F ASK BID = = = = Thus, the forward quotation is $: :

42 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 Spot rate rate = ra 1 r + r A B 1-42

43 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. 1-43

44 Interest Rate Parity Example Spot rate = $ per 90 day Forward rate = $ per 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 stronger, pound weaker Borrow British pounds ( ), transfer at Spot rate in dollars ($), invest in dollars ($), buy forward. 1-44