1. BA 282 Macroeconomics Class Notes - Part 3
Foreign Exchange
BA 282
Macroeconomics
Class Notes - Part 3
Foreign Exchange

2. 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
Japanese Yen (JPY) per US Dollar (USD)
Swiss Francs (CHF) per US Dollar (USD)
Foreign Exchange

3. 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
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4. 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.
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5. 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 Now what is the $ price of the bottle of wine if the dollar depreciates to 0.95 $/€ ?
Price in € before depreciation = $20 (1/0.85 $/€ ) = € 23.53
Price in $ after depreciation = € (0.95 $/€ ) = $ 22.35 or
Price in $ after depreciation = $20 (0.95/0.85) = $ 22.35
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6. 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 1.5 trillion USD
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7. 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
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8. For current rates see: http://online. wsj. com/documents/mktindex. htm
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9. 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.
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10. 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 $/€.
This obligates Boeing to deliver €110m to Citibank in 180 days in exchange for
€ 110m * $/€ = $ m
Foreign Exchange

11. 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
* 110m = $ 90.2m
* 110m = $ 95.7m
* 110m = $ 101.2m
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12. 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)
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13. FX Trading Statistics
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14. FX Derivative Market Stats
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15. JPY/USD
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16. Trade-Weighted USD Exchange Rate
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.
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17. USD/EUR
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18. 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?
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19. 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
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20. 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
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21. 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.
Foreign Exchange

22. 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
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23. 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
Foreign Exchange

24. 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
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25. 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?
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26. 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
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27. 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
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28. 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)
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29. 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
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30. 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
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31. 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%
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32. Plot the Points Exchange Rate ($/€) 0.9814 0.9615 0.9425
Expected Return on € Deposits
0.9241 2% 4% 6% 8%
Rate of Return ($)
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33. Graphical Equilibrium
Exchange Rate (LC/FC)
E0’’ 2 1
E0*
Expected Return on FC Deposits
E0’ 3
RLC
Rate of Return (LC)
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34. Changing LC Interest Rates and Exchange Rate Equilibrium
Exchange Rate (LC/FC) 1 1’ E0
LC Appreciates 2
Expected Return on FC Deposits
E0’
RLC
R’LC
Rate of Return (LC)
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35. Changing FC Interest Rates and Exchange Rate Equilibrium
Exchange Rate (LC/FC)
Rise in FC Interest Rate 2
E0’
LC Depreciates 1 E0
Expected Return on FC Deposits
RLC
Rate of Return (LC)
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36. 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
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37. Foreign Exchange

38. Money Market / Exchange Rate Linkages
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39. Foreign Exchange

40. Foreign Exchange

41. Foreign Exchange

42. Time path of US economic variables after a permanent increase in the US money supply
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43. FX & Currency Swaps
A swap is an agreement between two parties to exchange a predefined set of cashflows for a specified period.
A FX swap is the spot sale of a currency combined with a forward repurchase agreement (like a repo)
A simple currency swap is when one counterparty would agree to pay €10 million each year for five years. The other counterparty would agree to pay $8 million each year for five years.
Note that this currency swap is just a set of five forward contracts.
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44. FX & Currency Swap facts
Most currency swaps entail an up-front exchange of principal (unlike interest rate swaps)
Like FX forwards, most FX swaps have one side in USD
Currency swaps tend to be traded at longer maturities than forwards or options (> 1 year)
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45. FX Options
A call (put) option gives the owner the right but not the obligation to buy (sell) foreign currency at a prespecified exchange rate (called the strike) at a prespecified date.
An option allow the owner to participate in exchange rate changes in one-direction only
Consequently, options always have an upfront cost (called the premium)
For a US investor,
call options payoff when the USD/FCU exchange rate increases
put options payoff when the USD/FCU exchange rate decreases
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46. Calls and Puts Call Option Put Option X = Strike X = Strike
C0 = Call Premium
Net Payoff = max(E-X,0) - C0
Put Option
X = Strike
P0 = Put Premium
Net Payoff = max(X-E,0) - P0
Payoff
Payoff
USD/FCU
at Maturity X X
USD/FCU
at Maturity C0 P0
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47. Put Option Example
Put options are frequently used to “hedge” foreign exchange revenues
Back to Boeing example,
Recall Boeing expects to receive 110 million Euros in six months. Boeing calls Citibank and buys a 180-day put option with a strike of 0.85 $/€ for a premium of $2 million today.
When does Boeing exercise the put option?
Would the put option premium be more or less if the strike was 0.80 $/€?
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48. Changes in E0 and Expected Returns
How does a change in E0 (all else held constant) change the LC expected return of FC deposits?
Example:
E0 equals 1.00$/€ and Ee equals 1.05$/€.
Now suppose E0 increases to 1.03$/€
What happens to the dollar return on euros?
In general, a depreciation of the local currency results in a decrease in the local currency return of foreign currency deposits
Foreign Exchange