The Foreign
Exchange Market
(Part I)
Overview of the Lecture
1. Description of the foreign exchange
market
2. Rates and quotations
3. Currency arbitrage
© 2002 by Stefano Mazzotta
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1. Description of the
Foreign Exchange Market
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What is the foreign exchange
market?
• It is a set of banks, brokerage firms, and
dealers that brings buyers and sellers of
foreign exchange together.
• It is a system which allows institutions and
individuals
– to transfer purchasing power from one currency to
another,
– to engage in international transactions,
– to manage their exchange rate risk exposure.
© 2002 by Stefano Mazzotta
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Major markets
• United Kingdom, United States, Japan,
Germany, Switzerland, Singapore, Honk
Kong, France...
• All the time-zones are covered, from
Tokyo to San Francisco, through
London and New York.
© 2002 by Stefano Mazzotta
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Size of the market
• Average Daily volume in is about
$1,500,000,000,000
• Compare:
– NYSE - $30,000,000,000
– NASDAQ - $23,000,000,000
– TSE - $1,400,000,000
– Canada’s GDP - $605,000,000,000
© 2002 by Stefano Mazzotta
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Major participants
• Large commercial banks
– continuously making the market,
– receive compensation by making the “bidask” spread.
• Foreign exchange brokers
– facilitate trading between dealers,
– keep list of suppliers and demanders of
different currencies.
© 2002 by Stefano Mazzotta
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Other participants
• Central banks
– conduct intervention.
• Commercial entities
– regular but not continuous participants of the
market.
• Speculators and arbitrageurs
– trade to profit from the market itself.
© 2002 by Stefano Mazzotta
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Interbank market
• A highly liquid interbank market is formed
by an informal arrangement of large
commercial banks and foreign exchange
brokers.
• Day-to-day exchange rate day movements
is mainly the result of the activity of
interbank trades.
© 2002 by Stefano Mazzotta
Interbank market
transactions
• Spot transaction
– requires almost immediate delivery of foreign
exchange.
• Forward transaction
– requires delivery of foreign exchange at some
future date.
• Currency Swap transaction
– is the simultaneous purchase and sale of a foreign
currency .
© 2002 by Stefano Mazzotta
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Efficiency
• The foreign exchange market is very
efficient due to
– its 24-hour trading schedule
– extensive telecommunication network
– shear size of the market
– computerized quotation system
© 2002 by Stefano Mazzotta
2. Rates and Quotations
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Price quotes
• The prices are quoted in pairs:
– Bid - price at which the bank buys the currency
– Ask - price at which the bank sells the currency
– The spread, i.e. | bid – ask |, is the profit of the bank
(dealer)
• Home country based quotes:
– direct quote - a home currency price of a foreign
currency, e. g., EUR/USD in France
– indirect quote - a foreign currency price of home
currency, e. g., USD/EUR in France
© 2002 by Stefano Mazzotta
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Example
• The pound sterling is quoted at $1.6618-35.
• (This notation is a shorthand for 1.6618-1.6635
USD/GBP)
• What is the “bid-ask” spread?
1.6635 - 1.6618 = $0.0017
What is the spread in percentage points?
1.6635 - 1.6618
 100%  0.01%
1.6635
© 2002 by Stefano Mazzotta
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Example
• The pound sterling is quoted in New York at
$1.6618-35. This is a direct quote.
• What is the indirect quote?
1/1.6635  0.6011
1/1.6618  0.6018
• Therefore, the indirect quote is: 0.6011-18.
• What is the direct quote of a dollar in London?
© 2002 by Stefano Mazzotta
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Bid and ask quotes relation
• Suppose, there are 2 currencies: A and B.
• Then:
• And:
e(A/B) ASK
1

e(B/A) BID
e(A/B) BID
1

e(B/A) ASK
© 2002 by Stefano Mazzotta
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Example
• The bank quote for is 1.6050-72 SF/$
• What is the SF/$ exchange rate for a customer
who wants to exchange $ for SF?
e(SF/$) BID  1.6050
• What is the $/SF exchange rate for a customer
who wants to exchange SF for $?
e($/SF) BID
1
1


 0.6222
e(SF/$) ASK 1.6072
© 2002 by Stefano Mazzotta
The U.S. dollar based
quotations
• If currencies are quoted against USD, they
can be quoted in
– American terms: $ per unit of foreign currency
– European terms: units of foreign currency per 1$
• Nowadays, almost all except U.K. and Euro
exchange rates are expressed in European
terms.
© 2002 by Stefano Mazzotta
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Example
EXCHANGE RATES
Tuesday, February 6, 1990
The New York foreign exchange selling rates below apply to
trading among banks in amounts of $1 million and more, as quoted
at 3 p.m. Eastern time by Bankers Trust Co. Retail transactions
provide fewer units of foreign currency per dollar.
Currency
U.S. $ equiv.
per U.S. $
Country
Tues. Mon. Tues. Mon.
Britain (Pound) ...... 1.7015 1.7000 .5877 .5882
Canada (Dollar) ..... .8405 .8421 1.1897 1.1875
France (Franc) ...... .17709 .17718 5.6470 5.6440
Source: The Wall Street Journal
© 2002 by Stefano Mazzotta
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Cross rates
• Definition:
– Exchange rate between two foreign
currencies.
• Reason:
– Most currencies are quoted against the U.S. $
and not against each other.
• Result:
– The U.S. $ rate can be used to compute a
cross rate.
© 2002 by Stefano Mazzotta
Example of cross rate
quotation
• See http://money.cnn/markets/currencies
• See also http://www.bloomberg.com/markets/fxc.html
© 2002 by Stefano Mazzotta
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USD
Cross Rates 23 Dec
2002
GBP
CHF
JPY
CAD
AUD
EUR
NZD
DKK
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SEK
SEK 8.8943 14.18 6.2715 7.3879 5.7331 4.9990 9.1318 4.5917 1.2295
DKK 7.2342 11.53 5.1010 6.0090 4.6630 4.0660 7.4274 3.7347
NZD 1.9371 3.0879 1.3659 1.6090 1.2486 1.0887 1.9888
EUR 0.9740 1.5526 0.6868 0.8090 0.6278 0.5474
AUD 1.7792 2.8362 1.2546 1.4779 1.1468
CAD 1.5514 2.4731 1.0939 1.2887
JPY 120.39 191.91 84.89
CHF 1.4182 2.2608
GBP 0.6273
USD
0.8134
0.2678 0.2178
0.5028 0.1346 0.1095
1.8267 0.9185 0.2459 0.2000
0.8720 1.5928 0.8009 0.2145 0.1744
77.60 67.67 123.60 62.15 16.64 13.54
1.1780 0.9141 0.7971 1.4561 0.7322 0.1960 0.1595
0.4423 0.5211 0.4044 0.3526 0.6441 0.3239 0.0867 0.0705
1.5941 0.7051 0.8306 0.6446 0.5621 1.0267 0.5163 0.1382 0.1124
© 2002 by Stefano Mazzotta
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Example
• Let e(USD/EUR) = 0.97
• Let e(USD/CAD) = 0.63
• What is the EUR/CAD cross-rate?
1
e(EUR/CAD) 
 e(USD/CAD)
e(USD/EUR)
 e(EUR/USD)  e(USD/CAD)
 0.65
• So, 1 Canadian dollar can buy 0.65 euros.
© 2002 by Stefano Mazzotta
The general rule for cross
rates
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• Suppose, there are 3 currencies: A, B, and C.
• Suppose, the spot exchange rates e(A/B) and
e(B/C) are known.
• What is the cross exchange rate e(A/C)?
e(A/C)  e(A/B)  e(B/C)
© 2002 by Stefano Mazzotta
Cross rates and bid-ask
spreads
• With bid-ask spreads, the general rule
to compute cross rates is:
e(A/C) BID  e(A/B) BID  e(B/C) BID
e(A/C) ASK  e(A/B) ASK  e(B/C) ASK
© 2002 by Stefano Mazzotta
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Example: Question
• The spot quote for CHF/USD is 1.5150-72
• The spot quote for CAD/USD is 1.5810-56
• What is the direct spot quote for
CHF/CAD?
© 2002 by Stefano Mazzotta
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Example: Solution (part I)
e(CHF/CAD) BID  e(CHF/USD) BID  e(USD/CAD) BID
1
 e(CHF/USD) BID 
e(CAD/USD) ASK
1
 1.5150 
1.5856
 0.9555
© 2002 by Stefano Mazzotta
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Example: Solution (part II)
e(CHF/CAD) ASK  e(CHF/USD) ASK  e(USD/CAD) ASK
1
 e(CHF/USD) ASK 
e(CAD/USD) BID
1
 1.5172 
1.5810
 0.9596
• So, the direct spot CHF/CAD quote is 0.9555-96.
© 2002 by Stefano Mazzotta
3. Currency Arbitrage
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Currency arbitrage
• Definition:
– Realization of a riskless profit by
simultaneous buying a currency in one
market and selling it in another market.
• Cause:
– Exchange rate quote inconsistencies
across different money centers.
© 2002 by Stefano Mazzotta
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Example
• Bank of America’s quote of $1C is $0.705676.
• Royal Bank’s quote of $1C is $0.7038-52.
• How to make easy money?
• Buy $C from Royal Bank by paying $ and sell
$C to BoA receiving $.
• Make about $0.0004 per $ or $40 per
$100,000.
© 2002 by Stefano Mazzotta
Arbitrage exclusion
condition
• In the absence of taxes, etc., the
arbitrage exclusion condition is to
have overlapping bid-ask quotes.
Bid1
Ask1
Bid2
© 2002 by Stefano Mazzotta
Ask2
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Triangular arbitrage
• The essence:
– 1 unit of currency A buys currency B
– Currency B buys currency C
– Currency C buys more than 1 unit of currency A
AA
B
C
© 2002 by Stefano Mazzotta
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Example: part 1 - the set up
• The GBP is bid at 1.9809 in New York:
– e(USD/GBP) = 1.9809
• Swiss franc is offered at $0.6251 in Zurich:
– e(USD/CHF) = 0.6251
• London offers pounds sterling at CHF
3.1650:
– e(CHF/GBP) = 3.1650
• Amount of money: $1,000,000
© 2002 by Stefano Mazzotta
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Example: part 2 - the strategy
• Sell $1,000,000 in Zurich at e(USD/CHF) and
receive CHF 1,599,744.04.
• Sell these Swiss francs in London at
e(CHF/GBP) and receive GBP505,448.35.
• Sell the pounds sterling in New York at
e(USD/GBP) and receive $1,001,242.64.
• Net profit: $1,242.64
© 2002 by Stefano Mazzotta
Example: part 3 - market
adjustment mechanism
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• Large number of arbitrage transactions will
cause:
– Swiss franc to appreciate with respect to U.S.
dollar in Zurich
– Swiss franc to depreciate against the pound
sterling in London
– Sterling will fall in New York
• Markets adjust quickly and eliminate arbitrage
opportunities
© 2002 by Stefano Mazzotta
Triangular arbitrage
condition
• For triangular arbitrage to exist, the
following must hold:
1A  e(B/A) BID  e(C/B) BID  e(A/C) BID  1A
• Or, equivalently:
e(C/B) BID
1

e(B/A) BID  e(A/C) BID
© 2002 by Stefano Mazzotta
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Exercise
• To familiarize yourself with the currency spot
market sign up to:
–
http://fxgame.oanda.com/
– Take a position of your choice in ONE currency.
Individually.
– Take note of anything that you find interesting,
related or unrelated to what we discussed
– In one week we will have a class discussion of
your findings
© 2002 by Stefano Mazzotta