Exchange Rates

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					Foreign Exchange

      MBA 774
 Macroeconomics
Class Notes - Part 3




                       1
                      Foreign Exchange Rates
• The exchange rate is the price of one country’s
  currency in terms of another country’s currency
• Quoted exchange rates can be either direct or
  indirect, one method is usually the convention
  – Direct: home currency per unit of foreign currency
     • Examples from US perspective:
           1.676 US Dollars (USD) per British Pound (GBP)
           1.152 US Dollars (USD) per Euro (EUR)
  – Indirect: foreign currency per unit of home currency
     • Examples from US perspective:
           109.58 Japanese Yen (JPY) per US Dollar (USD)
           1.3664 Swiss Francs (CHF) per US Dollar (USD)
                                                            2
                    Prices in Foreign Currency

• Use the exchange rate in direct terms

  Example 1: How much does a €100 sweater cost an American
  if the exchange rate is 1.15 $/€?
             Price in $ = €100 * 1.15 $/€ = $115.00

  Example 2: How much does a 100 CHF sweater cost an
  American if the exchange rate is 1.37 CHF/$?
     Price in $ = 100 CHF * (1 / 1.37 CHF/$) = $72.99




                                                             3
                  Depreciation and Appreciation

• A depreciation of the local currency means that it
  takes more local currency to buy a unit of foreign
  currency
  – An appreciation of the local currency is the opposite


• Example:
  – If the $/€ exchange rate goes up from 1.10 to 1.20 the
    dollar has depreciated against the euro

  – but, the euro has appreciated against the dollar.

                                                             4
                           Depreciation and the
                             Price of Imports
• A depreciation of a country’s currency makes its
  goods cheaper for foreigners and makes foreign goods
  more expensive.
• Example: Consider a bottle of French wine that costs
  $20 when the $/€ exchange rate is 1.10. Now what is
  the $ price of the bottle of wine if the dollar
  depreciates to 1.20 $/€ ?
  Price in € before depreciation = $20 (1/1.10 $/€ ) = € 18.18
  Price in $ after depreciation = € 18.18 (1.20 $/€ ) = $ 21.82
  or
  Price in $ after depreciation = $20 (1.20/1.10) = $ 21.82

                                                                  5
                      Foreign Exchange Trading
• The vast majority of foreign exchange (FX) trading is
  done over-the-counter (OTC)

• Most transactions have the USD on one side
  – Dollar is called a vehicle currency

• Trading is centered at major multinational banks
  (called dealers) such as Citibank, Bank of America,
  Deutsche Bank, HSBC, etc.

• By volume, it is the largest market in the world
  – Average daily turnover is about 2 trillion USD
                                                          6
                     Foreign Exchange Trading
• Trading takes place 24 hours a day during the
  business week
• Trading moves around the globe:
     London => New York => Tokyo => London
• Other important participants are
  – Corporations
  – Nonbank financial institutions
  – Central banks
• For current rates see the Wall Street Journal or
  Bloomberg

                                                     7
                       Spot vs. Forward rates
• Spot Rate: the exchange rate that is applicable today
  – The settlement or value date for a spot transaction (the
    date on which the parties actually exchange assets) occurs
    two business days after the deal is made


• Forward Rate: the exchange rate agreed on today
  for a transaction at a future date.
  – Most commonly quoted 30, 90, or 180 days in the future.
  – The forward exchange rate is set so that no money changes
    hands today.


                                                                 8
                         Forward Example

• Boeing plans to deliver a 777 to KLM in six months
  and receive 110 million Euros. Boeing calls Citibank
  and enters into a 180-day forward contract at a
  forward rate of 1.2200 $/€.

• This obligates Boeing to deliver €110m to Citibank in
  180 days in exchange for
            € 110m * 1.220 $/€ = $134.200m



                                                          9
                       Why Use Forwards
• Suppose that Boeing did not enter into a forward
  agreement. What would be the dollar proceeds from
  the sale if in 6 months the Euro ends up trading at:

     USD/EUR              USD Proceeds
       1.12           1.12 * 110m = $123.2m
       1.22           1.22 * 110m = $134.2m
       1.32           1.32 * 110m = $145.2m



                                                     10
                        Derivative Securities
• A forward contract is the simplest form of a
  derivative security

• Definition: A derivative security is a financial
  contract that derives its value from the price of
  another underlying asset.

• Other common examples:
  – Swaps
  – Put and call options
  – Futures contracts (exchange-traded forwards)
                                                      11
                                  FX Trading Statistics


                                 Average Daily Volume
                                    (USD Billions)
Transaction Type
Spot Transactions                                         621
Forwards and Forex Swaps                                1,152
Currency Swaps                                             21
Options                                                   117
Correction for reporting errors                           -31
Estimated Total                                         1,880
Source: Bank for International Settlements




                                                                12
                         FX Derivative Market Stats
          The Global Foreign Exchange Derivatives Markets
         Notional Amounts Outstanding in Billions of US Dollars



Total contracts                                  24,475
  with other reporting dealers                     8,660
  with other financial institutions                9,450
  with non-financial customers                     6,365
  up to one year                                 18,840
  between one and five years                      3,901
  over five years                                 1,734

Memorandum Item:
 Exchange-traded Contracts                           132

Source: Bank for International Settlements


                                                                  13
                100
                      200
                            300
                                  400




            0
     19
       70


     19
       75


     19
       80


     19
       85


     19
       90


     19
       95


     20
                                        JPY/USD




       00


     20
       05
14
                                Trade-Weighted USD Exchange
                                           Rate
        150



        125



        100



          75



          50
           73



                       78



                                  83



                                              88



                                                          93



                                                                     98



                                                                                 03
         19



                     19



                                19



                                            19



                                                        19



                                                                   19



                                                                               20
The index is a weighted average of the foreign exchange values of the U.S. dollar against other major
currencies. The index weights, which change over time, are derived from U.S. export shares. The index is
calculated in indirect terms so higher values imply a stronger USD.
                                                                                                           15
     Jan




                0.80
                       0.90
                              1.00
                                     1.10
                                            1.20
                                                   1.30
                                                          1.40
         -99
      Jul
          -99
     Jan
         -00
      Jul
          -00
     Jan
         -01
      Jul
          -01
     Jan
         -02
      Jul
          -02
     Jan
         -03
      Jul
          -03
     Jan
         -04
      Jul
          -04
     Jan
         -05
      Jul
          -05
                                                                 USD/EUR




     Jan
         -06
      Jul
          -06
     Jan
         -07
16
                      The Law of One Price

• In competitive markets free of transportation costs
  and other barriers to trade, identical goods sold in
  different countries must sell for the same price
  (when expressed in the same currency).

• Why?




                                                         17
                     The Law of One Price
• We can write an equation for the law of one price as,
            PiLC = PiFC * E
  where
     PiLC is the local currency price of good i
     PiFC is the foreign currency price of good i
     E is the dollar to euro exchange rate

• Or we can rearrange the equation to get
          E = PiLC / PiFC


                                                      18
                 Purchasing Power Parity (PPP)
• PPP looks just like the law of one price except the
  prices are for a “basket” of goods rather than for a
  particular good so
             E = PLC / PFC
  or
             PLC = PFC * E
where
      PLC is the local currency aggregate price level
      PFC is the foreign currency aggregate price level


                                                          19
    Invented in 1986 as a light-hearted guide to
whether currencies are at their “correct” level,
burgernomics is based on the theory of purchasing-
power parity (PPP). This says that, in the long run,
exchange rates should move toward rates that would
equalise the prices of an identical basket of goods
and services in any two countries. To put it simply: a
dollar should buy the same everywhere. Our basket
is a McDonald's Big Mac, produced locally to roughly
the same recipe in 118 countries. The Big Mac PPP
is the exchange rate that would leave burgers
costing the same as in America. Comparing the PPP
with the actual rate is one test of whether a currency
is undervalued or overvalued.
    The first column of the table shows local-currency
prices of a Big Mac. The second converts them into
dollars. The average price of a Big Mac in four
American cities is $2.71. The cheapest burgers are
in China ($1.20); the dearest are in Switzerland
($4.52). In other words, the yuan is the most
undervalued currency, the Swiss franc the most
overvalued. The third column calculates Big Mac
PPPs. Dividing the local Chinese price by the
American price gives a dollar PPP of 3.65 yuan. The
actual exchange rate is 8.28 yuan, implying that the
Chinese currency is undervalued by 56% against the
dollar.
                                                     20
                  Purchasing Power Parity (PPP)
• PPP asserts that all countries’ price levels are equal
  when measured in terms of the same currency
  – Note: In practice the basket of goods is the same as the
    one used for the CPI


• PPP predicts that a decline (increase) in a currency’s
  domestic purchasing power will be associated with a
  proportional currency depreciation (appreciation) in
  the foreign exchange market



                                                               21
               Absolute PPP vs. Relative PPP

• Absolute PPP (PLC = PFC * E) represents the
  relationship between the level of the exchange
  rate and the level of prices in the two economies



• Relative PPP states that the percentage change in
  the exchange rate will be equal to the difference in
  the percentage change in the price levels in the
  two countries


                                                      22
                     Absolute PPP vs. Relative PPP

• We can write an equation for Relative PPP as

     (Et - Et-1)/ Et-1 = pLC,t – pFC,t

where
  pi,t is the inflation rate (Pi,t - Pi,t-1)/ Pi,t-1 in country i between
     time t-1 and t
  Et is the exchange rate at time t




                                                                        23
                     Empirical Evidence on PPP
• To test absolute PPP, we measure the price level of a
  basket of goods in various countries.
  – For example, The Economist’s Big Mac Index

• To test relative PPP we can look at the correlation
  between exchange rates and relative price levels
  – Typically correlations are low


• Empirically, PPP theory does poorly in predicting
  exchange rate movements for developed countries

• Why is it hard to test these theories?
                                                        24
                           Problems with PPP
• Transport costs and trade barriers
  – If it costs a substantial amount to transport goods, then
    this prevents the ability to do “arbitrage”
  – In some industries transport costs are effectively infinite
    (e.g., housing). These are called nontradable goods.
  – Governments usually have import tariffs, etc.

• Monopolistic or oligopolistic practices

• Measurement differences

• “Sticky” prices

                                                                  25
                   Demand for Foreign Currency

• If we think of foreign currency as a financial asset
  then the demand for foreign currency will depend on
  the investment properties of foreign currency

• For example, we might consider the following
  properties
  –   Expected Return
  –   Risk
  –   Liquidity
  –   Inflation

                                                     26
                    Demand for Foreign Currency
• For now we are going to concentrate on only one of these
   – Expected Return

• Notation
     RLC     Interest rate in local currency (e.g., USD)
     RFC     Interest rate in foreign currency (e.g., EUR)
     Et      Actual exchange rate at time t in LC/FC
     Ee      Expected exchange rate in one year
             (this is the expectation of a random variable)


                                                              27
                   Demand for Foreign Currency
• Definition: The annual rate of depreciation of LC
  relative to FC is the percentage increase in E over
  one year,
     rate of depreciation = (E1 - E0) / E0


• The LC rate of return on FC deposits is approximately
  RFC plus the rate of depreciation

• Today we do not know what E1 will be, only what we
  expect it to be (Ee). So,
     expected rate of return on FC = RFC + (Ee - E0) / E0
                                                            28
                          FX Market Equilibrium

• Equilibrium in the foreign exchange market is defined
  as
   difference in rate of return = RLC - RFC - (Ee - E0) / E0 = 0



• This is also called the interest parity condition and
  can be written as
                    RLC = RFC + (Ee - E0) / E0



                                                                   29
                      Graphing Interest Parity
• We can rearrange this equation so that
           E0 = Ee / (1 + RLC - RFC)
• Example: Suppose R€=5.2% and Ee=0.95 $/€, what is
  the exchange rate today (E0) for the following USD
  interest rates?
                  R$        E0
                  2%
                  4%
                  6%
                  8%
                                                       30
                     Plot the Points
Exchange Rate
($/€)




 0.9814




 0.9615

 0.9425
 0.9241                               Expected Return
                                      on € Deposits


                2%   4%   6%   8%   Rate of Return ($)



                                                         31
                Graphical Equilibrium
Exchange Rate
(LC/FC)




    E0’’         2


                       1
    E0*                    Expected Return
                           on FC Deposits
    E0’
                           3


                     RLC       Rate of Return (LC)



                                                     32
                       Changing LC Interest Rates and
                         Exchange Rate Equilibrium
         Exchange Rate
         (LC/FC)




                 E0          1     1’
LC Appreciates
                                   2    Expected Return
                 E0’
                                        on FC Deposits




                           RLC   R’LC    Rate of Return (LC)



                                                               33
                       Changing FC Interest Rates and
                         Exchange Rate Equilibrium
         Exchange Rate
                                Rise in FC
         (LC/FC)
                                Interest Rate




                 E0’                2
LC Depreciates
                 E0                 1
                                                    Expected Return
                                                    on FC Deposits


                                 RLC            Rate of Return (LC)



                                                                      34
                  Money, Interest Rates, & Exchange
                                Rates
• We can combine what we learned previously about
  the demand for money with what we now know about
  exchange rates

• This gives a more integrated picture of how money,
  interest rates, and exchange rates interact

• For convenience let’s rotate the money market graph
  clockwise 90o and combine it with the FX market
  graph

                                                       35
36
    Money Market /
Exchange Rate Linkages




                         37
38
39
40
Time path of US economic variables after a
permanent increase in the US money supply




                                             41