Contents
Glossary
Bruno Solnik/Dennis McLeavey 1
1. Currency Exchange Rates
Bruno Solnik/Dennis McLeavey 15
2. Foreign Exchange Parity Relations
Bruno Solnik/Dennis McLeavey 41
3. Foreign Exchange Determination and Forecasting
Bruno Solnik/Dennis McLeavey 89
4. International Asset Pricing
Bruno Solnik/Dennis McLeavey 131
5. Equity: Markets and Instruments
Bruno Solnik/Dennis McLeavey 171
6. Equity: Concepts and Techniques
Bruno Solnik/Dennis McLeavey 217
7. Global Bond Investing
Bruno Solnik/Dennis McLeavey 273
8. The Case for International Diversification
Bruno Solnik/Dennis McLeavey 331
9. Derivatives: Risk Mangement with Speculation, Hedging, and Risk Transfer
Bruno Solnik/Dennis McLeavey 379
10. Currency Risk Management
Bruno Solnik/Dennis McLeavey 431
11. Global Performance Evaluation
Bruno Solnik/Dennis McLeavey 469
12. Structuring the Global Investment Process
Bruno Solnik/Dennis McLeavey 527
Index 575
LEARNING OUTCOMES
After completing this chapter, you will be able to do the following:
■ Define direct and indirect methods of currency exchange rate quotations
■ Define and calculate the spread on an exchange rate quotation
■ Explain how spreads on exchange rate quotations can differ as a result of market conditions, bank/dealer positions, and trading volume
■ Convert direct (indirect) exchange rate quotations into indirect (direct) exchange rate quotations
■ Calculate cross rates, given two spot exchange rate quotations involving three currencies
■ Calculate the profit on a triangular
arbitrage opportunity, given the bid–ask quotations for the currencies of three countries
■ Distinguish between the spot and forward markets for currency exchange rates
■ Define and calculate the spread on a forward currency exchange rate quotation
■ Explain how spreads on forward currency exchange rate quotations can differ as a result of market conditions, bank/dealer positions, trading volume, and maturity/length of contract
■ Define forward discount and forward premium
■ Calculate a forward discount or premium on an exchange rate and express either as an annualized
rate
■ Explain covered interest rate
parity
■ Define and illustrate covered interest arbitrage
This chapter deals with foreign exchange quotes and the relationships between different types of quotes, as well as the nature of bid–ask spreads in the foreign exchange market. The exchange rate quotes for current and future delivery must be aligned with the risk-free interest rates in the two countries for which the quotes are given. This chapter presents the basic facts of foreign exchange involving quotation interpretation and arbitrage. Foreign exchange theories are saved for subsequent chapters.
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.
Before reviewing the international currency market, we will develop some basic notation. Over time, exchange rates change, so we will assume values for the current exchange rate, knowing that the actual values can be quite different by the time the reader views our printed page. Suppose now that we are told that the current exchange rate between the dollar ($) and the euro (:) is 0.8. That information is unhelpful because we have not been told whether this is a price quote for the dollar or for the euro.
By convention, we will present all quotes in this book 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, $:: = 0.8 indicates that one dollar is priced at 0.8 euros. Sometimes newspapers will report this as 0.8 euros per dollar. Conversely, we can also express the exchange rate between the dollar and the euro as ::$ = 1.25, where the euro is the quoted currency in units of dollars. The euro is priced at 1.25 dollars. Hence, we have Similarly, the dollar may be quoted as 120 Japanese yen (¥) per dollar, so that 100 yen are worth 0.8333 dollars. Quotations for the yen are usually indicated for 100 yen rather than for one yen because of the small value of the yen. Using the notation a:b, the quotations are 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 the various currency abbreviations that are commonly encountered. For example, the Japanese yen can be referred to as ¥, JPY,or yen.
In our discussion so far, we have used the natural terminology dollars per euro when referring to ::$ = 1.25 because the quoted currency is the euro. However, newspaper and trader terminology varies, and it is useful to be aware of different exchange rate treatments. It must be stressed that different news and trading are vices use different notations to refer to the same exchange rate. Actually, the notation $/: = 1.25, meaning 1.25 dollars per euro, is intuitive and we used this notation in previous editions, but we changed notation in the present edition to be consistent with what has become the most widely used convention. Readers familiar with
previous editions should be aware of the change in notation. To repeat, we will use ::$ to mean the price of one euro in dollars (number of dollars per euro). With this notation, the quoted currency is the first one (here, :) and its price is measured in units of the second currency (here, $).
Direct and Indirect Quotations As an exchange rate can be quoted with as the domestic currency or with as as the foreign currency, it is useful to introduce the nationality of the investor.
If a in a:b is the foreign currency and b the domestic currency, then the quote is terminated a direct quote naturally enough, the price of the foreign currency in which we are interested. An American investor seeing a quote ::$ = 1.25 expects to pay $1.25 for one euro. He is viewing a direct quote, the price of the foreign currency.
For the European investor, $:: = 0.8 is the direct quote that the price of one dollar is 0.8 euros.
If a in a:b is the domestic currency and b the foreign currency, then the quote is finished with an indirect quote, the amount of foreign currency that one unit of the domestic currency will purchase. To an
American investor, $:: = 0.8 indicates that one dollar (the domestic currency) will purchase 0.8 euros. To a European investor, ::$ = 1.25 indicates that one euro (the domestic currency) will buy $1.25.
A direct quote tells us how much it will cost to purchase amounts of foreign currency, and an indirect quote tells us how much foreign currency we can get for an amount of domestic currency. If a European must pay 100 dollars for an American product, he will use a direct quote $:: = 0.8 to know that it will cost him 80 euros. If a European is making a donation to a U.S. charity and wants to donate 100 euros, he will use an indirect quote ::$ = 1.25 to know that he is contributing 125 dollars.
Direct quotes and indirect quotes are reciprocals of each other. The price per unit of the foreign currency is the reciprocal of the number of units of foreign currency received for a unit of the domestic currency. Just as ::$ = 1.25 tells an American investor that one euro costs 1.25 dollars, so the reciprocal 1/::$ = 1/1.25 = $:: = 0.8 tells her that one dollar will purchase 0.8 euros. Of course, the direct euro quote for an American is the indirect dollar quote for a European, and vice versa.
Direct quotes and indirect quotes have directional differences when it comes to price appreciation. Because the direct quote tells us the price of the foreigner currency, an appreciation of the foreign currency causes an increase in the direct quote, but an appreciation of the foreign currency causes a decrease in the indirect quote. An appreciation of a currency is considered a strengthening and a depreciation of a currency is considered a weakening. The following table lays out these two alternatives for a foreign and domestic currency.
Cross-Rate Calculations A cross rate is the exchange rate between two currencies inferred from each country’s exchange rate with a third currency, the reference currency. From the quotation of two currencies against a reference currency, we can derive a cross exchange rate. Of use for us in manipulating exchange rates will be the recognition that the : sign in a:b can be interpreted as a “divide” sign, and we interpret a:b as b/a. Consider how two currencies, a and c, against a third, b, can give us a:c. In this form, a:b times b:c equals a:c. Of course, b:a times c:b then gives us c:a. Consider also how two currencies against a third a:b and a:c can give
us c:b. In this form, a:b divided by a:c equals c:b. Our conclusion then is that (a:b) , (a:c) = c :b (a:b) * (b:c) = a:c From the quotation of two currencies against the U.S. dollar, for example, we can derive the cross exchange rate between the two currencies: ::$ and $:¥ can give us ::¥. Assume that the euro is quoted as 1.25 dollars and the dollar is quoted as 120 Japanese yen (¥) per dollar. From these quotes, we can calculate the ::¥ rate. implies that (::$) × ($:¥) = ::¥, or In this example, one euro is worth 150 yen, or 100 yen are worth 0.6667 euros. Now consider the a:b and a:c case in the following quotes for the Korean won and the Brazilian real against the dollar, with $:won = 1012.5 and $:R$ = 2.297. We calculate the won per real rate equal to the won per dollar rate (2012.50) divided by the real per dollar rate: Forex Market and Quotation
Conventions The international currency market can be seen as having two components: ■ A worldwide foreign exchange (Forex) market where participants are major banks and specialized currency dealers (market makers). This is a “wholesale” interbank market for large transactions. ■ A “retail” market where investors and corporations deal with local banks. The Forex market is the driving force on the
currency market. Banks quote foreign exchange rates to their clients based on the Forex quotations. The Forex market is a worldwide market in which dealers, mostly large commercial and investment banks, trade large orders (typically several million dollars). This is an over-thecounter (OTC) market in which trading is done by telephone and on electronic platforms. Trading takes place 24 hours a day, 5 days a week. A typical daily transaction volume is well above $1 trillion, making it the largest and most liquid market in the world. In the Forex market, quotations are generally given with five significant digits and three-letter codes. For example, the USD:JPY quote could appear as 120.10 and the EUR:USD as 1.2515.1 The worldwide Forex market observes some specific trading conventions. First, there is no need to maintain a market in both euros against dollars and dollars against euros. For any pair of currencies, it is sufficient to trade in a single exchange rate. History mostly dictates the exchange rate direction that is selected. There is a decreasing order of seniority with the British pound as the senior currency. The Forex convention is to trade British pounds in units of other currencies, so the quote showing on Forex trading screens is the foreign
exchange value of one GBP, that is, GBP:EUR, GBP:USD, or GBP:JPY. For exchange rates involving the British pound, the quoted currency is always the pound. For example, the exchange rate between the pound and the dollar is quoted as the dollar price of one pound. When the euro was introduced in 1999, it was given “seniority” just behind its British neighbor. Thus, the quote showing on Forex trading screens is the foreign exchange value of one euro, EUR:USD or EUR:JPY. For exchange rates involving the euro, the quoted currency is always the euro except for the exchange rate with the pound, where the quoted currency is the pound. Finally, the dollar is quoted in units of all other currencies, for example, USD:JPY.2 Second, not all exchange rates are traded. In a world with a large number of currencies, there are a very large number of cross exchange rates. For example, with 20 currencies, there are 380 bilateral exchange rates. The exchange rates between two minor currencies are not traded on the Forex market, so a Forex trader could not find on her trading screen the exchange rate between the South Korean won (won or KRW) and the Brazilian real (R$ or BRL). There would be too few transactions between the won and
the real to maintain an active and liquid market. Actually, all currencies are simply traded against the U.S. dollar. To buy Korean won with Brazilian reals, an investor must do two Forex transactions: first buy dollars with reals, and then sell those dollars for won. To create liquidity on this interbank market, all transactions involving the Brazilian real are therefore conducted against the U.S. dollar. We can derive the cross rate won:R$ from the two exchange rates $:won and $:R$. Hence, all currencies are quoted against the U.S. dollar, which remains the dominant Forex currency of quotation, although there are such regional exceptions as the yen in Asia and the euro and pound in Europe.3 Third, Forex quotes always include a bid price and an ask price (or offer price), and there is no commission or fee added on a trade. The bid price is the price at which the foreign exchange dealer is willing to buy the quoted currency in exchange for the second currency. The ask price is the price at which the dealer is willing to sell the base currency in exchange for the second currency. The difference between the bid and the ask prices is referred to as the spread. As an example, assume that a dealer provides the following quote for the $:¥ (value of the dollar in
yen): $:¥ = 120.17–120.19 The dealer is willing to buy dollars at a price of 120.17 yen per dollar (bid) and willing to sell dollars at a price of 120.19 yen per dollar (ask). We now provide more details on bid–ask quotes. Bid–Ask (Offer) Quotes and Spreads As mentioned above, the foreign exchange dealer quotes not one but two prices. The bid price is the exchange rate at which the dealer is willing to buy a currency; the ask (or offer) price is the exchange rate at which the dealer is willing to sell a currency. The midpoint price is the average of the bid and ask price: (ask + bid)/2. The bid–ask spread is the difference between the bid and ask prices. For example, a bank could quote the euro in dollars as The dealer is willing to buy euros at a price of 1.2011 dollars per euro (bid) and willing to sell euros at a price of 1.2014 dollars per euro (ask). Forex traders would say that the spread is equal to 3 pips. A pip, which stands for price interest point, represents the smallest fluctuation in the price of a currency. Hence, a pip refers to one unit of the final digit of the quoted exchange rate. This is similar to the concept of “tick” for stocks. The spread is sometimes expressed as a percentage of the ask price (or midpoint price). In the example, the
percentage spread is about 2.5 basis points: Spreads differ as a result of market conditions and trading volume. The size of the bid–ask spread increases with exchange rate uncertainty (volatility) and lack of liquidity because of bank/dealer risk aversion. When a dealer posts a quote, she does not know whether the customer will buy or sell the quoted currency. Hence, the dealer could end up with an unexpected currency position, depending on the customer’s decision. It could take some time for the dealer to offset that position with another customer or on the Forex market. When markets are volatile, there could be a large adverse price movement during that time period. Dealers increase their quoted spreads in volatile times. For thinly traded currencies, it will take longer to offset a currency position at reasonable prices. The length of that time period increases the risk of an adverse price movement. Dealers quote larger spreads for illiquid currencies relative to major currencies with active trading. The bank/dealer position should not have a significant influence on the size of the bid–ask spread quoted by that dealer. Rather, the midpoint of the spread moves in response to dealer positions. For example, a dealer with excess supply
of a specific foreign currency would move the midpoint of that quoted currency down rather than adjust the size of his spread. A dealer quoting a large spread relative to other dealers will basically not trade, so that would not help to reduce the position. Neither will the dealer want to quote a smaller spread because that would mean raising his bid price when he does not want to buy. Basically, the dealer will lower both his bid and ask prices in order to induce customers to buy this specific currency rather than sell it. For example, a dealer with excess euros will try to sell them and therefore lower his ask price of $1.2014 to, say, $1.2012 and will probably also lower his bid to avoid having to buy more euros, from $1.2011 to, say, $1.2009. The Forex market quotes exchange rates only in one direction (e.g., ::$, not $::). But it is easy to infer the bid–ask prices for the same pair of currencies quoted in the other direction. Two principles apply: ■ The $:: ask exchange rate is the reciprocal of the ::$ bid exchange rate. ■ The $:: bid exchange rate is the reciprocal of the ::$ ask exchange rate. In the example above, the dealer is willing to buy euros for dollars at a bid price of 1.2011 dollars per euro. This would be equivalent of the dealer selling dollars
for euros at a rate of 1/1.2011 = 0.83257 euros per dollar. Hence, the ::$ quote of is equivalent to a $:: quote of A customer wishing to convert $100,000 into euros could simply buy the euros from the dealer at the ask price of ::$ = 1.2014 and hence obtain 100,000/1.2014 = :83,236. This is identical to selling $100,000 at the bid $:: = 0.83236. A local bank will happily quote bid–ask exchange rates in any direction requested by a customer. Of course, spreads quoted to “retail” customers tend to be wider than those found on the “wholesale” Forex market. Example 2 may help to show how a transaction is initiated.
Cross-Rate Calculations with Bid–Ask Spreads
Recall that a cross rate is the exchange rate between two currencies inferred from each currency’s exchange rate with a third currency, the reference currency. Earlier we examined a case of (a:b) ÷ (a:c) = c:b, where we assumed that the exchange rate of the Brazilian real per dollar was $:R$ = 2.2970 and that the won per dollar rate was $:won = 1012.50. We calculated the won per real cross rate by dividing the won per dollar rate (1012.50) by the real per dollar rate (2.2970): Let’s
now consider the case where currencies are quoted with a bid–ask spread, as follows: To compute bid–ask cross rates, we follow the same procedure but need to think of the direction of the money flow. For simplicity, assume that we are an investor interrogating a currency dealer. Hence, we take the view of a client, not of the dealer. First, think of the bid price as being the price when we (an investor) hold the quoted currency and want to sell it to the dealer, who is quoting us a price at which he is willing to purchase the quoted currency. Similarly, think of the ask price as the price when we want to buy the quoted currency from the dealer, who is
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