Notes on Mishkin Chapter 20
("Foreign Exchange Market")
Econ 353: Money, Banking, and Financial Institutions

Last Updated: 28 March 2015
Latest Course Offering: Spring 2011

Course Instructor:
Professor Leigh Tesfatsion
tesfatsi AT iastate.edu
Econ 353 Homepage:
http://www2.econ.iastate.edu/classes/econ353/tesfatsion/

  1. Exchange Rates and the Foreign Exchange Market
  2. Exchange Rates in the Long and Short Run
    1. Purchasing Power Parity (PPP)
    2. Interest Parity
  3. Pondering the Introduction of the Euro
    1. Historical Time-Line for Euro-Related Events
    2. Potential Benefits and Costs of Monetary Union
  4. Basic Concepts and Key Issues from Mishkin Chapter 20

I. Exchange Rates and the Foreign Exchange Market

An exchange rate is the price of one country's currency in terms of another. Consequently, exchange rates affect the relative cost of foreign versus domestic goods, services, and financial assets for a country.

Illustration:
An exchange rate E for the U.S. measures the price of a dollar in terms of a specified foreign currency. For example, if the foreign country is Japan, E is measured as yen per dollar; and if the foreign country is Germany, E is measured as euros per dollar.

From the viewpoint of any one domestic country, there is a different exchange rate for every foreign currency. In practice, summary measures are used to represent the average cost of foreign currencies for domestic citizens. In the U.S., for example, use is frequently made of effective exchange rate indices constructed as a weighted average of the exchange rates of various trading partners of the U.S., with the exchange rates of larger trading partners receiving relatively larger weights. Mishkin (Chapter 20, Figure 9) presents U.S. time series data for one such effective exchange rate from 1973 through 2008.

The international financial market where exchange rates are determined is called the foreign exchange market. This market is organized as an over-the-counter market run by several hundred dealers (typically banks) who stay in close contact with each other.

The most common type of transaction in the foreign exchange market involves the (approximately) immediate exchange of one currency for another, called a spot transaction. An exchange rate used in a spot transaction is called a spot exchange rate. In contrast, a forward transaction is an agreement to exchange currencies at some specified future date, and an exchange rate used in a forward transaction is called a forward exchange rate.

As stressed by Mishkin (Chapter 20), however, most trades in the foreign exchange market actually involve the buying and selling of bank deposits denominated in desired currencies rather than the direct buying and selling of currencies per se. Moreover, these trades consist of transactions in excess of $1 million. Smaller purchases of currencies for purposes such as travel must be obtained second-hand (and at higher cost) in the currency retail market from banks and other dealers who participate in the foreign exchange market.

Hereafter, for expositional simplicity, it is assumed that the world is divided into a home country (HC) and the rest-of-the-world (ROW). Following Mishkin (Chapter 20, footnote 2, p. 506), the exchange rate for the HC during any time period T, denoted by E(T), is always reported as ROW currency per HC currency unit.

Exchange Rate for the HC in Period T:

(1)    E(T)  =  Number of ROW currency units received
                in exchange for each HC currency unit
                in period T
           

Consequently, an increase in E(T) denotes a strengthening (or appreciation) of HC currency relative to ROW currency, in the sense that each HC currency unit now exchanges for more ROW currency units. Conversely, a decrease in E(T) denotes a weakening (or depreciation) of HC currency relative to ROW currency.

Given fixed prices in the HC and in ROW, the exchange rate E(T) determines the relative cost of goods, services, and financial assets in ROW versus the HC. For example, if E(T) increases (all else remaining the same), the goods, services, and financial assets in ROW become cheaper for HC citizens to buy, in the sense that one unit of HC currency now buys more of each of these ROW quantities than before.

However, the exchange rate E(T) is nominal in the sense that it does not take into account possible changes in the aggregate price levels in the ROW and the HC. To obtain a more accurate measure of the relative cost of goods, services, and financial assets in the ROW versus the HC, the nominal exchange rate needs to be transformed into a "real" exchange rate that corrects for such price changes.

Suppose the period-T aggregate price level in ROW -- denoted by PROW(T) -- is measured by the ROW GDP deflator (in ROW currency units). Similarly, suppose the period-T aggregate price level in the HC -- denoted by P(T) -- is measured by the HC GDP deflator in period T (in HC currency units).

Let "*" denote multiplication. Then the period-T real exchange rate for the HC, denoted by Er(T), is defined as follows:

Real Exchange Rate for the HC in Period T:


               E(T)*P(T)
(2)  E (T)  =  ---------
      r         PROW(T)


        E(T)*(Period-T price of HC production in HC currency)
   =  -------------------------------------------------------
         (Period-T Price of ROW production in ROW currency)


        Period-T price of HC production in ROW currency
   =    -----------------------------------------------   
        Period-T price of ROW production in ROW currency


         Period-T price
         of HC Production
      =  measured in terms   
         of period-T ROW
         production


Example: A Simple Illustration of Er(T):

Suppose the HC is the U.S., ROW is Japan, and T is the year 2010. Suppose, also, that only one good, wheat, is produced in both the U.S. and Japan. By specializing down to a consideration of only one good, the need to introduce aggregate price indices is avoided and the intended meaning of definition (2) for the real exchange rate is seen more clearly.

In addition, suppose


 Y(2010)    =  U.S. real GDP  =  6 bushels of U.S. wheat ;

 YN(2010)   =  U.S. nominal GDP  =  12 USD;

 P(2010)    =  U.S. price of U.S. wheat

            =  YN(2010)/Y(2010)  (U.S. GDP deflator)

            =  12 USD/[6 bushels of U.S. wheat]

            =  2 USD per 1 bushel U.S. wheat;

 E(2010)    =  U.S. Exchange Rate

            =  1.5 yen per 1 USD;

 PROW(2010) =  yen price of Japanese wheat

            =  4 yen per 1 bushel Japanese wheat;

 2010 transport costs, import duties, etc. = 0

Then

                      1.5 yen          2 USD
  E(2010)*P(2010)  =  ------- * -------------------
                       1 USD    1 bushel U.S. wheat
               
                   =  3 yen per 1 bushel U.S. wheat
    
                   =  yen price of U.S. wheat ;

and


  1/PROW(2010)  =  1/4 bushel Japanese wheat per yen .


Hence, supressing the period indicator 2010 for ease of notation,


       E*P     1.5 yen          2 USD          1/4 bushel J wheat
E  =  ----- =  ------- * ------------------- * -------------------
 r    PROW      1 USD    1 bushel U.S. wheat         1 yen

                         
      3/4 bushels of J wheat     Price of 1 bushel U.S. wheat
   =  ----------------------  =  measured in terms of J wheat  .
      1 bushel U.S. wheat

II. Exchange Rates in the Long and Short Run

KEY POINT: As stressed by Mishkin (Chapter 20, p. 505), the basic trick to understanding what effect a factor has on the movement of exchange rates is to keep in mind the following common-sense observation: If a change in some factor shifts to the right the demand curve for domestically produced goods and services, then (all else equal) the demand curve for domestic currency will also shift to the right. The result will be an appreciation in the domestic currency relative to foreign currency.

Can anything more be said? In particular, assuming traders in the foreign exchange market are "rational" profit-seekers, can arbitrage conditions (i.e., conditions ensuring all profit opportunities are fully exploited) be used to predict more carefully the movement of exchange rates in the long and short run? This question is explored in the next two subsections.


II.A Purchasing Power Parity

Suppose that the HC and ROW always produce exactly the same bundle of goods and services, that there are no barriers to trade (i.e., no transportation costs, import duties, quotas, etc.), and that all traders are perfectly informed about the availability of goods and services in both the HC and ROW.

In this case, one would expect to find that the value of HC production measured in ROW currency units is exactly the same as the value of ROW production measured in ROW currency units. That is, recalling (2), one would expect to find that the following purchasing power parity (PPP) condition holds:

Basic Purchasing Power Parity Condition:

(3)

E * P = PROW , or equivalently, Er = 1

For how could differences in valuation persist for identical bundles of goods and services, apart from barriers to trade, if profit-seeking traders are rational? ROW and HC buyers would presumably always seek out the goods and services with the lowest prices (using either all ROW currency evaluations or all HC currency evaluations), which would tend to drive E*P and PROW into approximate equality. This is often referred to as the law of one price.


Example: A Simple Illustration of Purchasing Power Parity

Recall, again, the numerical example given above in which the real exchange rate turned out to be 3/4 bushels of Japanese wheat per 1 bushel of U.S. wheat.

In this example, the dollar price of a bushel of U.S. wheat (given by P) is 2 USD, and the dollar price of a bushel of Japanese wheat (given by PROW/E - why?) is 2.67 USD. Moreover, the yen price of a bushel of U.S. wheat (given by E*P) is 3 yen and the yen price of a bushel of Japanese wheat (given by PROW) is 4 yen. Consequently, a bushel of U.S. wheat is cheaper than a bushel of Japanese wheat, measured either in U.S. dollars or in yen.

Suppose that U.S. wheat and Japanese wheat are precisely the same physical good (same quality, same taste, etc.). Then, in the absence of all barriers to trade, residents of Japan would desire to purchase cheaper U.S. wheat rather than Japanese wheat, which which would put upward pressure on E*P, the yen price of a bushel of U.S. wheat.

This upward pressure on E*P, the yen price of a bushel of U.S. wheat, would presumably continue until E*P just equals PROW, the yen price of a bushel of Japanese wheat. At this point the PPP holds, i.e., , the real U.S. exchange rate Er = E*P/PROW equals 1. Also, at this point the nominal U.S. exchange E is given by E = PROW/P = [4 yen/2 USD] = 2 yen per USD.

Note that E*[P/PROW]=1 can also be expressed as P = PROW/E, i.e., the dollar price P of a bushel of U.S.wheat equals the dollar price PROW/E of a bushel of Japanese wheat.


An interesting alternative way of expressing the PPP condition (3) is in terms of rates of change.

Suppose that the PPP condition (3) holds from T to T+1, which implies that the real exchange rate Er = E*P/PROW remains constant (at 1) over this time interval. This constancy can hold only if E*P and PROW are growing at exactly the same rate over time. The latter condition guarantees that any percentage increase or decrease in E*P is exactly offset by an equal percentage increase or decrease in PROW, keeping the value of the ratio E*P/PROW constant.

Moreover, it can be shown that the rate of change of any product X*Y is equal to the sum of the separate rates of change of X and Y. Consequently, another way of expressing the assumption that the ratio E*P/PROW remains constant from T to T+1 is as follows:


      Rate of Change of E*P   =   Rate of Change of PROW
        from T to T+1                from T to T+1

or

      E(T+1)-E(T)        P(T+1)-P(T)           PROW(T+1) - PROW(T)
      -----------   +    -----------     =    -------------------
         E(T)               P(T)                    PROW(T)

    Rate of change       Inflation Rate in      Inflation Rate in
    in the HC exchange   in the HC from T       ROW from T to T+1
    rate E from T        to T+1
    to T+1

Subtracting the HC inflation rate from each side of this equation, one obtains the following interesting relation:

Alternative Form for the Purchasing Power Parity Condition (3):



       E(T+1)-E(T)      PROW(T+1)-PROW(T)       P(T+1)-P(T)
(4)    -----------  =   -----------------   -   -----------  .
          E(T)               PROW(T)                P(T)

    Rate of change       Inflation Rate in    Inflation Rate in
    in the HC exchange   ROW from T to T+1    in the HC from T
    rate E from T to T+1                      to T+1


The PPP condition in the rate-of-change form (4) has the following important implication. If inflation is higher in ROW than in the HC, then the HC currency should be appreciating in the sense that E(T+1) is greater than E(T). And conversely, if inflation is lower in ROW than in the HC, then the HC currency should be depreciating.

This makes intuitive sense, since (all else remaining the same) the relatively higher rate of increase in the ROW price level should cause ROW citizens to increase their demand for HC goods, services, and financial assets relative to those in ROW, which puts upward pressure on the HC exchange rate.

Mishkin (Chapter 20, Figure 2) presents time series evidence for the U.S. and United Kingdom that supports the PPP condition in form (4) over the long run, i.e., when the data points are averaged over fairly long periods of time (e.g., 20 years).

Unfortunately, this same evidence also indicates that the PPP condition (4) does not necessarily hold over shorter periods of time. This failure has been disappointing to advocates of flexible exchange rates, because volatility in real exchange rates can disrupt the operations of firms specializing in exports and imports.

The key reason why real exchange rates fail to remain constant over short periods of time is that currency demands and supplies depend on factors in addition to foreign and domestic aggregate price levels for tradable goods and services. Some of these factors are listed below.

Consequently, whether in form (3) or form (4), to date the PPP condition has not provided an adequate explanation of how real exchange rates are determined in the short run.

Although the PPP theory does not permit the accurate prediction of short-run movements in real exchange rates, a second type of arbitrage (profit exploitation) condition -- interest parity -- has helped in practice to guide these predictions. This condition is taken up in the next subsection.


II.B Interest Parity (cf. Mishkin, Chapter 20, Appendix)

Empirically, it has long been noted for the U.S. that real interest rates and exchange rates tend to move together relative to their "norms" -- i.e., either both are higher than normal or both are lower. For example, Mishkin (Chapter 20, Figure 9) presents time series evidence for the U.S. from 1973 through 2008 that shows this positive co-movement between real interest rates and one particular effective exchange rate index (i.e., a weighted average of the exchange rates for various major trading partners of the U.S.).

What underlying factors might explain this observed positive correlation between real interest rates and exchange rates?

The first important point to note is that changes in exchange rates can open up exploitable profit opportunities from pure currency "swaps" -- e.g., switching from ROW to HC currency now in anticipation of a later switch back from HC to ROW currency. Consider the following example.


Example: A Perceived Arbitrage Opportunity Arising from a Perceived Increase in the HC Real Exchange Rate

Suppose wheat is the only good produced in both the U.S. and Japan, and suppose the following conditions hold in some period T:

Then the U.S. real exchange rate Er satisfies


             3/4 bushels of Japanese wheat
  E (T)  =  ------------------------------  ;
   r             1 bushel U.S. wheat


    1       4/3 bushels of U.S. wheat
  -----  =  -------------------------  .
  E (T)     1 bushel Japanese wheat
   r


Suppose that a Japanese investor with 100 yen in period T anticipates a rise in the U.S. real exchange rate from T to T+1. Specifically, suppose that the Japanese investor expects to see

      e          1 bushel of Japanese wheat
     E (T+1)  =  --------------------------  .
      r             1 bushel U.S. wheat

Then the Japanese investor can conduct the following arbitrage: In period T, use the 100 yen to buy 25 bushels of Japanese wheat. Exchange these 25 bushels of Japanese wheat for [25*4/3] = 100/3 bushels of U.S. wheat. Then, in period T+1, convert the 100/3 bushels of U.S. wheat back to [(100/3)*1] = 33.3 bushels of Japanese wheat. If his expectations are correct, the Japanese investor will then end up with [33.3 - 25] = 8.3 additional bushels of Japanese wheat in period T+1. He can then sell these 33.3 bushels in exchange for [33.3 bushels] * [4 yen/bushel] = 132.2 yen, giving him a net profit of 32.2 yen.


The possibility of making money from pure currency swaps affects the flow of international financial investments. To see this more carefully, consider the case of investing in ROW versus HC deposit accounts.

Let the real interest rate on an investment in an HC bank deposit account held from T to T+1 be denoted by rHC(T) and let the real interest rate on an investment in a ROW bank deposit account held from T to T+1 be denoted by rROW(T). For simplicity, suppose that transaction costs are zero and that the risk characteristics of ROW bank deposit accounts and HC bank deposit accounts are the same.

In considering whether to put his money into a ROW bank deposit account for one period, from T to T+1, the ROW resident will consider the ROW real interest rate rROW(T). However, in considering whether to put his money into an HC bank deposit account for one period, from T to T+1, the ROW resident must consider both the HC real interest rate rHC(T) and the rate of change in the HC real exchange rate from T to T+1 given by


           E (T+1) - E (T)
(7)         r         r
          -----------------    .
                E (T)
                 r

Any increase (decrease) in Er from T to T+1 represents a gain (loss) to the ROW investor in and of itself. This is so because the ROW resident must convert HC currency back to ROW currency in order to repatriate any earnings from his HC bank deposit account.

If Er stays constant from T to T+1, the change from ROW currency to HC currency in period T and back to ROW currency in period T+1 is a wash in and of itself -- that is, ignoring interest payments, the ROW investor neither gains nor loses ROW purchasing power on this currency transaction. However, if Er increases (or decreases) from T to T+1, the ROW investor gains (or loses) ROW purchasing power on each unit of ROW currency exchanged.

Assuming there are no barriers to currency flows between the HC and ROW, we would therefore expect interest parity to hold between the HC and ROW in the following sense:

Interest Parity (Real Form):

                       e
                      E (T+1) - E (T)]
                       r         r
(8)     rHC(T)   +   -----------------          =   rROW(T)  .
                           E (T)
                            r

  Real interest      Expected real return rate   Real interest
  rate from T to     on HC currency held from    rate from T
  T+1 on HC bank     T to T+1                    to T+1 on ROW
  deposit accounts                               bank deposit
  secured with HC                                accounts secured
  currency in T                                  with ROW currency
                                                 in T

Suppose, for example, that the real interest rates in the HC and ROW from T to T+1 are given by rHC(T) = .10 and rROW(T) = .05, respectively. Seeing the 5 percent HC real interest rate advantage, should a ROW resident put his money into an HC bank deposit account from T to T+1 rather than a ROW bank deposit account from T to T+1?

The answer depends on whether or not the ROW resident expects the HC real exchange rate Er to depreciate by more than 5 percent from T to T+1, thereby offsetting the 5 percent HC real interest rate advantage. If this expected depreciation rate is more than 5 percent, he should choose a ROW bank deposit account, and if it is less than 5 percent, he should choose an HC bank deposit account. If the expected depreciation is exactly 5 percent, he will be indifferent between the two options. [Recall that the risk characteristics of ROW and HC bank deposit accounts are assumed to be identical.]

An important implication of the interest parity condition (8) is that the HC real interest rate rHC will tend to be high relative to the ROW real interest rate rROW when investors anticipate that the HC currency is going to depreciate, i.e., that Er(T+1) is going to be smaller than Er(T). But an anticipated depreciation in the HC exchange rate is exactly what one would expect to occur when the HC currency is stronger than normal -- that is, when the HC exchange rate is currently high relative to its historic norm.

Bottom Line: The interest parity condition (8) helps to explain why, empirically, real interest rates and exchange rates tend to move together over time.

In (8), rHC and rROW are real interest rates, hence the appropriate exchange rate in (8) is the real exchange rate Er. If the real interest rates rHC and rROW are instead replaced with nominal interest rates iHC and iROW for the HC and ROW, then the real exchange rate in (8) should be replaced with the nominal exchange rate E for the HC. Consequently, the interest parity condition (8) in nominal form is as follows:

Interest Parity (Nominal Form):


                       e
                      E (T+1) - E (T)
(9)    iHC(T)   +   -----------------   =   iROW(T)  .
                           E(T)

  Nominal interest   Expected nominal      Nominal interest
  rate from T to     return rate on HC     rate from T to
  T+1 on HC bank     currency held from    T+1 on ROW bank
  deposit accounts   T to T+1              deposit accounts
  secured with HC                          secured with ROW
  currency in T                            currency in T


NOTE: Mishkin (Chapter 20, Appendix, pp. 525-528) provides a derivation of the interest parity condition in equation (9) form. Mishkin (Chapter 20, 509-514) provides an extensive discussion illustrating how the interest parity condition in form (9) can be used to help understand and predict actual exchange rate movements.

To understand how (9) is derived from (8), use the fact that the expected rate of change for the real exchange rate Er from T to T+1 -- the second expression appearing in (8) -- is approximately given by


        e                 e                   e
       E (T+1)-E(T)      P (T+1) - P(T)      P ROW(T+1)-PROW(T)
(10)    -----------  +  ---------------  -  ------------------- .
           E(T)              P(T)                 PROW(T)

      Expected rate    Expected inflation    Expected inflation
      of change in     rate in HC from T     rate in ROW from T
      the HC nominal   to T+1                to T+1
      exchange rate
      E from T to T+1

Replacing the expected rate of change of Er in (8) by expression (10), and recalling that the nominal interest rate is given by the sum of the real interest rate and the expected inflation rate, one obtains the desired nominal form (9) for the interest parity condition.

Finally, combining (9) with the PPP condition (4) expressed in expectational form, one obtains a relation expressing the famous international Fisher effect:

International Fisher Effect:


                          e                   e
                         P (T+1)-P(T)     PROW (T+1)-PROW(T)
(11)  iHC(T)-iROW(T)  =  ------------  -  ------------------ .
                             P(T)              PROW(T)


In short, under conditions in which purchasing power parity and interest parity both hold over time, any difference in nominal interest rates between the HC and ROW will be equal to the difference in their expected inflation rates because the real interest rates in the HC and in ROW will be the same.

III. Pondering the Introduction of the Euro

Note: This section expands on the brief discussions of the European Union and euro-related issues provided by Mishkin in Chapters 20 and 21.

The European Union (EU) currently (1 July 2013) consists of 28 member countries. To date, only 17 of these 28 EU member countries belong to the eurozone (or euro area), standardly interpreted to mean the subset of EU member countries that have adopted the euro as their only currency. The remaining 10 EU member countries have not (yet) adopted the euro as their only currency.

The 17 EU member countries that currently have adopted the euro as their only currency are: Austria, Belgium, Cyprus, Estonia, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, Malta, the Netherlands, Portugal, Slovakia, Slovenia, and Spain.

The eleven EU member countries that currently have not adopted the euro as their only currency are: Bulgaria, Croatia, Czech Republic, Denmark, Hungary, Latvia, Lithuania, Poland, Romania, Sweden, and the United Kingdom.

The euro is also used by countries and regions outside of the EU (e.g., Monaco, San Marino, and Vatican City). Some commentators apply the term "eurozone" to all regions that have adopted the euro as their only currency, but this is not standard usage and will not be adopted here.

A. Historical Time-Line for Euro-Related Events

B. Potential Benefits and Costs of Joining the Eurozone

Potential Benefits:

Potential Costs:

III. Basic Concepts and Key Issues from Mishkin Chapter 20

Basic Concepts:

Key Issues:

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