Ch. 7: Exchange Rates and the Foreign Exchange Market

Part B of the course (international monetary economics) starts with the basics of exchange rates and the foreign exchange (forex) market, Feenstra and Taylor Chapter 13. The lecture has five parts: (1) exchange rate essentials (definitions, appreciation and depreciation, multilateral exchange rates, comparing prices); (2) exchange rates in practice (fixed and floating regimes); (3) the market for foreign exchange (spot contracts, transaction costs, derivatives, actors, government intervention); (4) arbitrage and spot exchange rates; and (5) arbitrage and interest rates (covered and uncovered interest parity). Interest parity is the key building block for the short-run theory of the exchange rate; the next chapter supplies the long-run building block.

Defining the exchange rate

Always check the units. Every exchange rate can be expressed in two ways, one the inverse of the other. If one euro costs $1.15, E $/€ = 1.15: this is the "American terms" (what Americans pay in dollars for one euro). One dollar is then worth 1/1.15 = €0.87, so E €/$ = 0.87: the "European terms" (what Europeans pay in euros for one dollar). (The slide writes the inverse with the same subscript $/€; the correct label for 0.87 is €/$.)

Newspaper tables of exchange rate quotations show, for each currency, the rate per dollar, per pound and per euro, today and a year earlier. For example on 1 June 2007 the euro was quoted at 0.745 per dollar (so $1.342 per euro), against 0.780 per dollar ($1.282 per euro) a year earlier; the yen was 122.0 per dollar and 163.8 per euro.

Appreciation and depreciation

• A currency appreciates against another currency if it buys more of that currency.
• A currency depreciates if it buys less of that currency.

Example: E $/€ rises from $1.06 to $1.28. A euro now buys 0.22/1.06 = 20.8% (about 21%) more dollars: the euro has appreciated by about 21% against the dollar, and the dollar has depreciated.

Multilateral exchange rates: the NEER

A bilateral exchange rate shows the price at which one currency is exchanged for another. A currency can appreciate against one currency while depreciating against another, so to understand the average change in its value we need a multilateral exchange rate. The nominal effective exchange rate (NEER) measures the value of a currency against a basket of foreign currencies, where the weight of each currency is its country's share in the home country's trade in a base year.

How much has the dollar fallen? (Headlines, 2002 to 2005). The dollar depreciated strongly against some key currencies (the Fed major currency index, a basket of 7 currencies, fell from 100 to the mid 70s), but much less against its trading partners as a whole (the Fed broad index of 26 currencies fell only to the mid 80s). The major floating currencies (UK, Japan, Canada, euro) rose against the dollar, while many other trading partners (China, India) kept more or less fixed exchange rates against the dollar, so the trade-weighted fall was smaller.

Using exchange rates to compare prices in a common currency

Prices in different countries can only be compared after converting them into a common currency. The UK price in dollars is E $/£ × P UK (units: $/£ times £ = $). The lecture example: James Bond's next tuxedo costs £2,000 in London, HK$30,000 in Hong Kong and $4,000 in New York. Converted into pounds:

Lessons: exchange rates let us compare prices in the same currency, and changes in exchange rates change the relative prices of goods across countries. An appreciation of the home currency raises the relative price of its exports to foreigners and lowers the relative price of imports; a depreciation lowers the relative price of its exports and raises the relative price of imports.

Exchange rate regimes: fixed versus floating

• Fixed (pegged) exchange rate: the exchange rate does not fluctuate at all, or only within a narrow band, against a base currency for a sustained period (usually a year or longer). Government intervention in the forex market is needed to maintain it.
• Floating (flexible) exchange rate: the exchange rate fluctuates over time, and the government makes no attempt to peg it. Appreciations and depreciations can occur yearly, monthly, daily or by the minute, and the volatility differs greatly among floating regimes.

Developed countries: there is much short-run volatility; the US dollar floats against the yen, the pound and the Canadian dollar (the "loonie"), and the euro behaves similarly. The Danish krone keeps a band of plus or minus 2% against the euro through intervention by the Danish central bank.

Developing countries: exchange rates tend to be more volatile. Some adopted fixed rates but were forced to abandon the peg after an exchange rate crisis. Many use intermediate regimes: a managed float (preventing dramatic changes without committing to a strict peg) or a crawl (the exchange rate follows a preset trend rather than a fixed level).

There are official (de jure) and actual (de facto) regimes: some countries say they float but in practice peg. Rather than two categories there is a continuum: free floating, managed floating, crawls and bands, and hard pegs with no movement. A very hard peg can take the form of a currency board, with special rules. Some countries have no currency of their own.

Currency unions and dollarization. A currency is used in more than one country in two cases: a currency union, in which a group of countries agrees to use a common currency, usually with a joint monetary policy (the eurozone); and dollarization, in which a country unilaterally adopts another country's currency and has no influence over its monetary policy (for example Ecuador).

The market for foreign exchange

The forex market has no central organised exchange: trading is over the counter (OTC), bilaterally between two parties. It is huge: about $3.2 trillion a day in April 2007. The main centres, London, New York and Tokyo, account for more than half of all transactions, and trading is spread over most time zones.

The spot contract. Two parties agree to exchange one currency for another for delivery on the spot at a set price, the spot exchange rate. Default risk is very low because settlement is almost instantaneous. Spot trades account for nearly 90% of all forex transactions; personal transactions are a very small share.

Transaction costs. The spread is the difference between the "buy at" and "sell for" prices. It is a market friction that creates a wedge between the price paid by the buyer and the price received by the seller, and it reflects the intermediaries between an individual and the central market. Spreads are larger for individuals than for banks and corporations trading large volumes.

Derivatives are contracts whose price derives from the spot rate. They let investors trade foreign exchange for delivery at different times or under different contingencies, altering payoffs and the risk of a portfolio: hedging (risk reduction) or speculation (risk taking).

Example 1: hedging. The CFO of a US firm expects to receive €1 million in 90 days for exports to France. The spot rate is $1.10 per euro, and the firm would make severe losses if the euro weakened below $1 per euro. The CFO buys options giving the right to sell the €1 million for dollars at $1.05 per euro (an option to buy dollars with euros). This insures that the euro receipts sell for at least $1.05, guaranteeing a profit on the deal even if the spot rate falls below $1.05.

Example 2: speculation. One-year euro futures are priced at $1.20. You expect the dollar to depreciate to $1.32 per euro in a year, so you buy the futures. If you are right, you earn (1.32 minus 1.20)/1.20 = 10%; any rate above $1.20 gives a profit. If the rate is at or below $1.20, the futures investment is a loss (the slide describes it as a total loss).

Private actors. The key players are forex traders at big commercial banks, trading electronically between bank accounts in different currencies (interbank trading). The top 5 banks account for about 50% of the market and the top 10 for about 75%. Bank deposits are the most important influence in the market. Other players are major corporations (multinationals) and nonbank financial firms (such as mutual funds); by trading directly they avoid bank fees, which is worthwhile only if their volume is large.

Government intervention. Governments may impose capital controls to limit trading, establish an official market at government-set rates (which usually creates a black market with illegal trades at different rates), or even try to outlaw trading. Most often they rely on less drastic intervention, usually by the central bank buying and selling currency to influence the price.

Arbitrage and spot exchange rates

Arbitrage is a trading strategy that exploits price differences. Its purest form involves no risk and no capital: a riskless profit. Market equilibrium is defined by the no-arbitrage condition: there are no riskless profit opportunities.

Arbitrage with two currencies. Suppose the dollar is quoted at £0.50 in New York and £0.55 in London. A New York trader sells $1 in London for 55p and uses it to buy 55/50 = $1.10 in New York: an instant riskless profit of 10%. As traders do this, demand for dollars in New York raises the pound price of the dollar there, and the extra supply of dollars in London lowers it there, until the two rates converge. In today's markets equalisation happens very quickly; only minuscule spreads (less than 0.1%) remain, due to transaction costs. No arbitrage requires E £/$ in New York = E £/$ in London.

Arbitrage with three currencies (triangular arbitrage). The cross rate relates exchange rates expressed in different currencies: E £/$ = E £/€ × E €/$. Selling dollars directly for pounds must give the same result as selling dollars for euros and then euros for pounds.

Vehicle currencies. Most currency pairs are traded through a third currency because direct trades between two minor currencies are rare. The third currency is a vehicle currency. In April 2007 the US dollar was on one side of 86% of all forex transactions; the euro, yen and pound also serve as vehicle currencies.

Arbitrage and interest rates

Exchange rate risk is the change in the value of an asset due to a change in the exchange rate. There are two kinds of arbitrage between deposits in different currencies:

• Riskless arbitrage: the investor covers the exchange rate risk with a forward contract. The no-arbitrage condition is covered interest parity (CIP).
• Risky arbitrage: the investor does not cover the risk and invests based on the current and the expected future exchange rate. The no-arbitrage condition is uncovered interest parity (UIP).

Covered interest parity (CIP)

The forward exchange rate F is the price of a forward contract. It lets investors holding foreign currency deposits be certain today about the future home-currency value of those deposits. Consider investing $1 for one year. In New York it grows to (1 + i $) dollars. In Europe, $1 buys 1/E $/€ euros today, which grow to (1 + i €)/E $/€ euros; converting them back at the forward rate gives (1 + i €) × F $/€/E $/€ dollars, with no exchange rate risk.

Evidence on CIP. The profit from a covered position between German marks and British pounds, 1970 to 1994, is (1 + i GER) × F UK/GER/E UK/GER minus (1 + i UK): the pound return on German deposits minus the pound return on UK deposits. The data show large deviations (profits up to more than 10% a year) in the 1970s, which disappeared after the UK abolished capital controls in 1979 and Germany in 1981. In liberalised financial systems riskless arbitrage opportunities have disappeared: CIP holds apart from tiny spreads, and the CIP equation is used to price forward contracts exactly.

Assets and their attributes (side bar)

Investors' demand for assets depends on three attributes: the rate of return (the total net increase in wealth from holding the asset for a period; higher is preferred), risk (the volatility of the return; lower is preferred) and liquidity (the ease and speed of selling the asset for cash; higher is preferred). Investors trade off among them, for example accepting more risk and less liquidity for a higher return. Because most returns are not guaranteed, expectations matter: investors act on the expected rate of return.

Uncovered interest parity (UIP)

Now the investor does not use a forward contract. The $1 invested in Europe gives (1 + i €) euros per 1/E $/€, converted back at the future spot rate, which is unknown today. The investor forms an expectation E e $/€ and expects (1 + i €) × E e $/€/E $/€ dollars; there is exchange rate risk.

CIP plus UIP. If both hold, the right-hand sides must be equal, so F $/€ = E e $/€: the forward rate equals the expected future spot rate. Intuition: if F differed from E e, one party to the forward contract would prefer to wait and trade at the more favourable expected spot rate (if investors are risk neutral).

A testable implication. Subtracting 1 from both sides of F/E = E e/E gives: F $/€/E $/€ minus 1 (the forward premium, positive or negative: how much more or less investors pay for the forward than for the spot) = E e $/€/E $/€ minus 1 (the expected rate of depreciation of the dollar). Researchers measure expectations with surveys of forex traders and plot the expected depreciation against the forward premium. UIP plus CIP predicts a 45-degree line. Surveys find a positive slope close to 1, but with much noise because traders' beliefs differ widely. UIP therefore finds some support.

Summary: how spot and forward rates are determined

What remains to be explained is where the expected future exchange rate E e comes from. That requires a theory of the exchange rate in the long run: purchasing power parity and the monetary approach (next chapter).