[See also the handout (to be distributed in class Mon. 4/14), titled "Understanding Exchange Rates: Supply & Demand in the Foreign Exchange Market."  It contains basically all the foreign-exchange-market graphs we saw in class.]

In these notes:
I.    Introduction to the foreign exchange market
II.  Currency conversions
III. Returns on international assets
IV. Supply and demand in the foreign exchange market  

I. INTRODUCTION TO THE FOREIGN EXCHANGE MARKET

Most countries have their own currencies, and when people in different countries do business with each other, an exchange of currencies must take place. For example, suppose you're vacationing in London and you walk into a pub and order a pint of ale.  No bartender in Britain is going to let you pay your tab in dollars -- you're going to have to get a hold of some British pounds sterling. More generically, you're going to have to get a hold of some foreign exchange.

FOREIGN EXCHANGE: all currencies other than the domestic currency(in our case, all currencies other than the dollar). The foreign exchange market refers to any and all places where different currencies are traded for one another.

EXCHANGE RATE: the price of one country's currency in terms of another country's currency; the rate at which two currencies are traded for another.
-- Exchange rates for all of the world's major currencies are listed daily in the Wall Street Journal.
---- [We saw a currency-rates table from x-rates.com.  It showed exchange rates between the dollar and several foreign currencies.]
---- Ex.: On March 17, 2003, the U.S.-Canadian exchange rate was .6757 U.S. dollars per Canadian dollar (i.e., a Canadian dollar costs you 67.57 cents), or 1.4799 Canadian dollars per U.S. dollar.

A note on usage: The term "exchange rate" has probably generated more confusion than any other term in economics (no small feat). When economists talk of "the exchange rate," it's often unclear which exchange rate they're talking about. To be more precise, identify what currency you're talking about:
* the dollar's exchange rate = price of a dollar in terms of a foreign currency
* the foreign exchange rate = price of a foreign currency in terms of dollars
-- Note that each one is the reciprocal (1/X) of the other

A still-better idea is to avoid the term "exchange rate" altogether. Instead, we can talk of currency appreciation and depreciation. Namely,
* A currency APPRECIATES when it increases in value
    (i.e., it becomes more expensive, it purchases more foreign currency).
* A currency DEPRECIATES when it decreases in value
     (i.e., it becomes cheaper, it purchases less foreign currency).

To further avoid vagueness, don't say "the exchange rate appreciates" -- say "the dollar appreciates."

II. CURRENCY CONVERSIONS

To know how much an item produced in one country will cost in another country's currency (i.e., as an import or to a tourist), you need to change the unit of account (e.g., dollars, francs) by performing a currency conversion.

For any good or service produced outside the U.S., the price in dollars is:

P_{in dollars} = P_{in foreign currency units} * dollars/(unit of foreign currency)

For any good or service produced in the U.S., the price in terms of foreign currency is:

P_{in foreign currency units} = P_{in dollars}* (units of foreign currency)/dollar

The key is to get it into the right unit of account -- on the right-hand side of the equation, the other currency units should cancel out.

-- Ex.:
(Suppose the dollar trades for 0.6847 British pounds, and 1 British pound trades for 1.4606 dollars.)
Q: How much would a Cadbury chocolate bar (made in Britain) that sells for one British pound go for in U.S. dollars?
A: P_{in dollars} = P_{in pounds} * dollars/pound = 1 pound * 1.4606 dollars/pound = 1.4606 dollars (or $1.4606)
---- (Note how the pound units just drop out of the equation, as the units term becomes [pound*dollar]/pound = dollar.)

-- Ex.:
Q: How much would a $10 bottle of California wine cost in Japan?
A: (From the "Currency Trading" table, we can see that 1 dollar trades for 118.46 Japanese yen, and 1 Japanese yen trades for .008442 dollars.  Now we just need to plug the appropriate one of those numbers -- the yen-per-dollar ratio -- into the formula.)
      P_{in yen} = P_{in dollars}* yen/dollar = 10 dollars * 118.46 yen/dollar = 1184.6 yen
---- (Note how the dollar units drop out of the equation.)

III. RETURNS ON INTERNATIONAL ASSETS

When international investors consider whether to invest in one country or another, they must take into account not only the nominal returns (RETs) on investments in the different countries, but also the exchange rates and how they might change over time.  The real return involves two currencies, not one -- for example, if you are an American who is investing in European stocks, a depreciation of the euro relative to the dollar would lower the return on your investment, just as higher inflation in Europe would lower the real return for a European who has invested in European stocks.

--> The relevant return for an international investor is the
(real, after-tax) return after all currency exchanges have taken place.
          |
(So as not to complicate this lecture unnecessarily, we will ignore the effect of inflation and taxes on RET in all the equations and examples that follow.)

-- For U.S. holders of foreign assets, the real return is higher if the foreign currency appreciates against the dollar.
RET on foreign asset held by an American
= nominal RET on asset + appreciation of foreign currency
= nominal RET on asset - appreciation of U.S. dollar

-- For foreign holders of U.S. assets, the real return is higher if the dollar appreciates against the foreign currency.
RET on U.S. asset held by a foreigner
= nominal RET on asset + appreciation of U.S. dollar
= nominal RET on asset - appreciation of foreign currency

The rate of appreciation of a currency is calculated as a percent change. The dollar's rate of appreciation, for example, would be:

                                   (New P_dollar) - (Old P_dollar)
appreciation of dollar = ---------------------------------- * 100%
                                                 Old P_dollar

                                     { New P_dollar       }
                                 =  {---------------- - 1 } * 100%
                                     {  Old P_dollar        }

Ex.:
At its inception in January 2000, the euro traded at a rate of 1.15 U.S. dollars per euro.  In March 2003, it cost 1.10 U.S. dollars per euro.  The euro's total rate of appreciation
    { 1.10         }
= {------ - 1   } * 100% = (.957-1) * 100% = (-.043) * 100% = -4.3%
    { 1.15         }

If an American purchased Volkswagen (German) stock in January 2000 and earned 15% (in euro terms) between then and March 2003, his total return, net of currency exchanges, would be

To calculate the annualized, or yearly, rate of appreciation of the euro, just apply the annualized-rate-of-increase formula that we've used earlier in this coures.  Compute the ratio of the euro's new exchange price divided by its old exchange price, and take that ratio to the power of 1/n, where n is the number of intervening years.  In this case, it was 3 years and 2 months, so n = 3 + 2/12 = 3.17.
-- Formula:
            annualized appreciation of euro = {[(New P_euro)/(Old P_euro)]^(1/n) - 1} * 100%
-- Applied to above example:
            annualized appreciation of euro = {[(1.10/1.15)^(1/3.17)-1} = {(.957)^(1/3.17)-1} = .986-1 = -.014 = -1.4%)

IV.  UNDERSTANDING EXCHANGE RATES: SUPPLY & DEMAND IN THE FOREIGN EXCHANGE MARKET

[Refer to the three-page handout from class, titled "Understanding Exchange Rates:  Supply & Demand in the Foreign Exchange Market."  (I'm not posting it online because {1} you have it already and {2} graphs are prohibitively hard to put up on the Internet.)  The handout is supposed to offer a relatively simple explanation of what causes currencies to appreciate or depreciate.  See also the "Exchange Rates in the Short Run" unit on pp. 232-37 of the textbook, which also uses supply-and-demand diagrams of the foreign-exchange markets.]