Homework's Mathematical Methods
leon weng
Session3-Part1-chapter2.pptxIntroduction to Exchange Rates and the Foreign Exchange Market
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Exchange Rate Essentials
Exchange Rates in Practice
The Market for Foreign Exchange
Arbitrage and Spot Exchange Rates
Arbitrage and Interest Rates
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2 Exchange Rates in Practice
Exchange Rate Regimes: Fixed Versus Floating
There are two major types of exchange rate regimes—
fixed and floating:
Fixed (or pegged) exchange rates fluctuate in a narrow range (or not at all) against some base currency over a sustained period. A country’s exchange rate can remain rigidly fixed for long periods only if the government intervenes in the foreign exchange market in one or both countries.
Floating (or flexible) exchange rates fluctuate in a wider range, and the government makes no attempt to fix it against any base currency. Appreciations and depreciations may occur from year to year, each month, by the day, or every minute.
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FIGURE 2-2 (1 of 2)
This figure shows the exchange rates of three currencies against the U.S. dollar. The U.S. dollar is in a floating relationship with the yen, the pound, and the Canadian dollar. The U.S. dollar is subject to a great deal of volatility because it is in a floating regime, or free float.
APPLICATION
Exchange Rate Behavior: Selected Developed Countries, 1996-2012
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FIGURE 2-2 (2 of 2)
This figure shows exchange rates of three currencies against the euro, introduced in 1999. The pound and the yen float against the euro. The Danish krone provides an example of a fixed exchange rate. There is only a tiny variation around this rate, no more than plus or minus 2%. This type of fixed regime is known as a band.
APPLICATION
Exchange Rate Behavior: Selected Developed Countries, 1996-2012 (continued)
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FIGURE 2-3 (1 of 2)
Selected Developing Countries, 1996-2012 Exchange rates in developing countries show a wide variety of experiences and greater volatility. Pegging is common but is punctuated by periodic crises (you can see the effects of these crises in graphs for Thailand, South Korea, and India). India is an example of a middle ground, somewhere between a fixed rate and a free float, called a managed float.
APPLICATION
Selected Developing Countries, 1996-2012
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FIGURE 2-3 (2 of 2)
Colombia is an example of a crawling peg. The Colombian peso is allowed to crawl gradually, it steadily depreciates at an almost constant rate for several years from 1996 to 2002. Dollarization occurred in Ecuador in 2000, which is when a country unilaterally adopts the currency of another country.
APPLICATION
Selected Developing Countries, 1996-2012 (continued)
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3 The Market for Foreign Exchange
Exchange rates the world over are set in the foreign exchange market (or forex or FX market).
The forex market is not an organized exchange: trade is conducted “over the counter.”
In April 2013, the global forex market traded, $5.3 trillion per day in currency.
The four major foreign exchange centers are located in the United Kingdom (London), the United States (New York), Singapore, and Japan (Tokyo).
Other important centers for forex trade include Hong Kong, Paris, Sydney, and Zurich.
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The simplest forex transaction is a contract for the immediate exchange of one currency for another between two parties. This is known as a spot contract.
The exchange rate for this transaction is often called the spot exchange rate.
The use of the term “exchange rate” always refers to the spot rate for our purposes (i.e. in this class).
The spot contract is the most common type of trade and appears in almost 90% of all forex transactions.
The Spot Contract
3 The Market for Foreign Exchange
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Derivatives
FIGURE 2-5
In addition to the spot contracts other forex contracts include forwards, swaps, futures, and options.
Collectively, all these related forex contracts are termed derivatives.
The spot and forward rates closely track each other.
3 The Market for Foreign Exchange
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Foreign Exchange Derivatives
Forwards
A forward contract differs from a spot contract in that the two parties make the contract today, but the settlement date for the delivery of the currencies is in the future, or forward. The time to delivery, or maturity, varies. However, because the price is fixed as of today, the contract carries no risk.
Swaps
A swap contract combines a spot sale of foreign currency with a forward repurchase of the same currency. This is a common contract for counterparties dealing in the same currency pair over and over again. Combining two transactions reduces transactions costs.
APPLICATION
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Foreign Exchange Derivatives
Futures
A futures contract is a promise that the two parties holding the contract will deliver currencies to each other at some future date at a prespecified exchange rate, just like a forward contract. Unlike the forward contract, futures contracts are standardized, mature at certain regular dates, and can be traded on an organized futures exchange. Hence, the future contract does not require that the parties involved at the delivery date be the same two parties that originally made the deal.
Options
An option provides one party, the buyer, with the right to buy (call) or sell (put) a currency in exchange for another at a prespecified exchange rate at a future date. The buyer is under no obligation to trade and will not exercise the option if the spot price on the expiration date turns out to be more favorable.
APPLICATION
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Most forex traders work for commercial banks. About 3/4th of all forex transactions globally are handled by just 10 banks.
The exchange rates for these trades underlie quoted market exchange rates.
Some corporations may trade in the market if they are engaged in extensive transactions in foreign markets.
Private Actors
Some governments engage in policies that restrict trading, movement of forex, or restrict cross-border financial transactions are called a form of capital control.
In lieu of capital controls, the central bank must stand ready to buy or sell its own currency to maintain a fixed exchange rate.
Government Actions
3 The Market for Foreign Exchange
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4 Arbitrage and Spot Exchange Rates
FIGURE 2-6
Arbitrage and Spot Rates Arbitrage ensures that the trade of currencies in New York along the path AB occurs at the same exchange rate as via London along path ACDB. At B the pounds received must be the same, regardless of the route taken to get to B:
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In general, three outcomes are again possible.
The direct trade from dollars to pounds has a better rate: E£/$ > E£/€ E€/$
The indirect trade has a better rate: E£/$ < E£/€ E€/$
The two trades have the same rate and yield the same result: E£/$ = E£/€ E€/$. Only in the last case are there no profit opportunities. This no-arbitrage condition:
Arbitrage with Three Currencies
The right-hand expression, a ratio of two exchange rates, is called a cross rate.
4 Arbitrage and Spot Exchange Rates
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FIGURE 2-7
Arbitrage and Cross Rates Triangular arbitrage ensures that the direct trade of currencies along the path AB occurs at the same exchange rate as via a third currency along path ACB. The pounds received at B must be the same on both paths:
4 Arbitrage and Spot Exchange Rates
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The majority of the world’s currencies trade directly with only one or two of the major currencies, such as the dollar, euro, yen, or pound.
Many countries do a lot of business in major currencies such as the U.S. dollar, so individuals always have the option to engage in a triangular trade at the cross rate.
When a third currency, such as the U.S. dollar, is used in these transactions, it is called a vehicle currency because it is not the home currency of either of the parties involved in the trade and is just used for intermediation.
Cross Rates and Vehicle Currencies
4 Arbitrage and Spot Exchange Rates
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5 Arbitrage and Interest Rates
An important question for investors is in which currency they should hold their liquid cash balances.
Would selling euro deposits and buying dollar deposits make a profit for a banker?
These decisions drive demand for dollars versus euros and the exchange rate between the two currencies.
The Problem of Risk
A trader in New York cares about returns in U.S. dollars. A dollar deposit pays a known return, in dollars. But a euro deposit pays a return in euros, and one year from now we cannot know for sure what the dollar-euro exchange rate will be.
Riskless arbitrage and risky arbitrage lead to two important implications, called parity conditions.
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Contracts to exchange euros for dollars in one year’s time carry an exchange rate of F$/ € dollars per euro. This is known as the forward exchange rate.
If you invest in a dollar deposit, your $1 placed in a U.S. bank account will be worth (1 + i$) dollars in one year’s time. The dollar value of principal and interest for the U.S. dollar bank deposit is called the dollar return.
If you invest in a euro deposit, you first need to convert the dollar to euros. Using the spot exchange rate, $1 buys 1/E $/€ euros today.
These 1/E $/€ euros would be placed in a euro account earning i €, so in a year’s time they would be worth (1 + i €)/E$/€ euros.
Riskless Arbitrage: Covered Interest Parity
5 Arbitrage and Interest Rates
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To avoid that risk, you engage in a forward contract today to make the future transaction at a forward rate F$/€.
The (1 + i €)/E$/€ euros you will have in one year’s time can then be exchanged for (1 + i €)F$/€/E$/€ dollars, or the dollar return on the euro bank deposit.
Riskless Arbitrage: Covered Interest Parity
This is called covered interest parity (CIP) because all exchange rate risk on the euro side has been “covered” by use of the forward contract.
5 Arbitrage and Interest Rates
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FIGURE 2-8
Arbitrage and Covered Interest Parity Under CIP, returns to holding dollar deposits accruing interest going along the path AB must equal the returns from investing in euros going along the path ACDB with risk removed by use of a forward contract. Hence, at B, the riskless payoff must be the same on both paths:
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5 Arbitrage and Interest Rates
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In this case, traders face exchange rate risk and must make a forecast of the future spot rate. We refer to the forecast as , which we call the expected exchange rate.
Based on the forecast, you expect that the euros you will have in one year’s time will be worth when converted into dollars; this is the expected dollar return on euro deposits.
The expression for uncovered interest parity (UIP) is:
Risky Arbitrage: Uncovered Interest Parity
5 Arbitrage and Interest Rates
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FIGURE 2-10
Arbitrage and Uncovered Interest Parity Under CIP, returns to holding dollar deposits accruing interest going along the path AB must equal returns from investing in euros going along the risky path ACDB. Hence, at B, the expected payoff must be the same on both paths:
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5 Arbitrage and Interest Rates
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The UIP approximation equation says that the home interest rate equals the foreign interest rate plus the expected rate of depreciation of the home currency.
Suppose the dollar interest rate is 4% per year and the euro 3%. If UIP is to hold, the expected rate of dollar depreciation over a year must be 1%. The total dollar return on the euro deposit is approximately equal to the 4% that is offered by dollar deposits.
Uncovered Interest Parity: A Useful Approximation
5 Arbitrage and Interest Rates
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What Determines the Spot Rate?
Uncovered interest parity is a no-arbitrage condition that describes an equilibrium in which investors are indifferent between the returns on unhedged interest-bearing bank deposits in two currencies.
We can rearrange the terms in the uncovered interest parity expression to solve for the spot rate:
Risky Arbitrage: Uncovered Interest Parity
5 Arbitrage and Interest Rates
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Evidence on Uncovered Interest Parity
Dividing the UIP by the CIP, we obtain , or .
Although the expected future spot rate and the forward rate are used in two different forms of arbitrage—risky and riskless, in equilibrium they should be exactly the same!
If both covered interest parity and uncovered interest parity hold, the forward must equal the expected future spot rate.
Investors have no reason to prefer to avoid risk by using the forward rate, or to embrace risk by awaiting the future spot rate.
APPLICATION
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