ECON352 - International Finance
Module 2 - Exchange Rates and Foreign Exchange Market
Part B: Arbitrage
Haiping Zhang
Department of Economics
University of Auckland Business School
Overview
Lecture 2A introduces the essential elements of exchange rates and FX markets.
This lecture introduces a key concept – Arbitrage.
1. Major FX Instruments
A. Spot and Forward Contracts
B. The Bid-Ask Spread
2. Intratemporal Arbitrage (across markets)
3. Intertemporal Riskless Arbitrage (over time)
2
What is traded on the world FX markets?
Foreign Exchange Market Turnover by Instrument (Daily Average in April)
Source: OTC foreign exchange turnover in April 2022, The 2022 BIS Triennial Central Bank Survey
3
1.A Spot and Forward Contracts
• The Spot Rate:
the price for an “immediate” exchange, i.e.,
the delivery within one or two working days
after the exchange is agreed.
Date of Delivery
Date
0
1
2
Date of contract
• The Forward Rate: the price for a “future”
exchange, i.e., the delivery at a specified time
in the future (30, 90, 180, … days from now).
Date
0
Date of contract
N
• The term “exchange rate” refers to the spot
rate in this course, unless otherwise noted.
• FX swap is the combination of a spot
contract & a forward contract in the
opposite direction.
 Buy a particular currency (e.g., USD)
using the spot rate in today’s market,
 sell the same currency (USD) 90 days
later using the 90-day forward rate in
today’s market.
• The spot contract is the most common type
of trade and appears in nearly 79% of all
forex transactions in 2019 and in 2022.
Date of Delivery N=7,
14, 21, 30,60, 90, …
4
1.B The Bid-Ask Spread
Base
Currency
Spot
Rate
Bid Price
NZDUSD = 0.6612 /18
Quote
Currency
Ask Price
• Caution: Quote conventions in textbooks vs.
FX markets/policy.
• Bid Price vs. Ask Price
• The Gap between the Two Prices
5
1.B The Bid-Ask Spread
Wholesale Banks
(Market Makers)
Bid (Buy) Price:
the dealer is willing to buy 1 NZD
(the Base Currency) at 0.6612 USD.
Retail Banks
FX Brokers
Ask (Sell, Offer) Price:
the dealer is willing to sell 1 NZD
(the Base Currency) at 0.6618 USD.
Individual Traders
FX Trading Platform
Tourists
• The gap between the ask price and the bid price is called the spread.
In this example, the spread = 0.0006 or 6 pips (percentage in points).
At any point in time, the ask price > the bid price. Why?
• Spreads are an example of market frictions or transaction costs that create a wedge between
the price paid by the buyer and the price received by the seller.
The US dollar as the vehicle currency, Revisiting the international role of the US dollar, BIS, 2022
6
Overview
Lecture 2A introduces the essential elements of exchange rates and FX markets.
This lecture introduces a key concept – Arbitrage.
1. Major FX Instruments
2. Intratemporal Arbitrage (across markets)
A. Arbitrage with Two Currencies
B. Triangle Arbitrage (with Three Currencies)
3. Intertemporal Riskless Arbitrage (over time)
7
2.A Intratemporal Arbitrage Across Markets: Two Currencies
Quiz: Suppose that British pound and the US dollar are traded today in New York and in London at
𝐋𝐨𝐧𝐝𝐨𝐧
𝐍𝐘
the exchange rate of 𝐄£/$
= 0.7 and 𝐄£/$
= 0.72, respectively. You have 100 US dollars.
• Can you make a profit in the two markets? How much is the profit per round of arbitrage?
• If all FX traders take the same trading strategy, how do exchange rates move in the two markets?
Solution Procedures:
1. Identify the base currency for the exchange rates: USD
2. In which market is the BC more expensive? London
3. Can you make a profit in this case? Buy low sell high (buy USD in NY & sell it in London)
4. If you have US$ 100, how much profit (in USD terms) can you make per round of arbitrage?
𝐋𝐨𝐧𝐝𝐨𝐧
𝐍𝐘
Gross return: $100 * 𝐄£/$
/ 𝐄£/$
= $100 * 0.72 / 0.7 = $102.86 Profit: $102.86-$100=$2.86
5. If all FX traders take the same trading strategy, how do the market demand and supply change?
the market demand for (supply of) the USD rises in NY (London).
6. How do exchange rates move in New York and in London?
the exchange rate of the USD rises in NY and falls London
=> FX rate converges in the two markets => the Law of One Price applies.
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2.A Intratemporal Arbitrage Across Markets: Two Currencies
Arbitrage with Spot Rates: Arbitrage ensures that the trade of currencies in New York along the
path AB occurs at the same exchange rate as via London along path ACDB.
At B, the pounds received must be the same, regardless of the route taken to get to B.
The Law of
One Price
Why do we multiple the amount
of the USD by the exchange rate to
calculate the amount of the GBP?
Because we sell the base currency.
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2.A Intratemporal Arbitrage Across Markets: Two Currencies
In the absence of transaction costs (cross-country transfer fee and the bid-ask spread),
• an FX rate differential => an arbitrage opportunity, while
• arbitrage eventually eliminates the FX rate differential.
Quiz: What if there is a positive spread between the ask and bid prices in each market?
Case 1:
𝐋𝐨𝐧𝐝𝐨𝐧
E£/$
= 0.6985/95
𝐍𝐘
E£/$
= 0.6980/90
𝒊
𝐄£/$
0.6995
0.6990
0.6985
0.6980
Case 2:
𝐋𝐨𝐧𝐝𝐨𝐧
E£/$
= 0.6985/95
𝐍𝐘
E£/$
= 0.6970/80
Any arbitrage opportunity?
C
D
𝒊
𝐄£/$
Any arbitrage opportunity?
A
0.6995
A
B
0.6985
0.6980
C’
B
0.6970
D’
Market
NY London
Market
NY London
10
2.B Intratemporal Arbitrage Across Markets: Three Currencies
Quiz: Today’s exchange rates in London are E£/$ = 0.7, E€/$ = 0.8, and E£/€ = 0.9.
Suppose you have USD 100. Can you make a profit by trading the three currencies?
Two alternative routes of converting $ into £.
1. Direct route:
USD 100 = E£/$ * $100 = 0.7*100 = £ 70
[Selling the BC => multiply the amount of BC by the FX rate]
2. Indirect route:
A. Exchange $ into €: USD 100 = E€/$ * $100 = 0.8*100 = € 80
B. Exchange € into £: € 80 = E£/€ * € 80 = 0.9*80 = £72
3. What is your trading strategy? Buy low sell high
𝐃𝐈𝐑
a) Buy low: use £ to buy $ via the direct route (𝐄£/$
= 0.7) and
𝐈𝐍𝐃
b) Sell high: sell $ for £ via the indirect route (𝐄£/$
= 0.72 )
c) How much is your profit (in USD terms) per round of arbitrage?
𝐈𝐍𝐃
𝐃𝐈𝐑
$100 * 𝐄£/$
/ 𝐄£/$
−$𝟏𝟎𝟎 = $100 * 0.72 / 0.7 −$𝟏𝟎𝟎 = $2.86
Compare this quiz with the one on page 8: differences and similarities?
11
2.B Intratemporal Arbitrage Across Markets: Three Currencies
• If all the FX traders take the same trading strategy, how do the FX rates change?
• Are there any profit opportunities in the long run?
The Law of
One Price
Sell the BC => multiply
Sell the BC => multiply
Sell the BC => multiply
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Application: Algorithmic Trading and Arbitrage Opportunities
• How quickly could the exchange rates reach the equilibrium?
Milliseconds are focus in algorithmic trades, 11 May 2007, Reuter.
Algorithmic trading in Foreign Exchange: Increasingly sophisticated, BNP Paribas, June 2023
[Application Programming Interface]
[Electronic Broking Services]
Source: The foreign exchange market, 2023, BIS
13
Overview
Lecture 2A introduces the essential elements of exchange rates and FX markets.
This lecture introduces a key concept – Arbitrage.
1. Major FX Instruments
2. Intratemporal Arbitrage (across markets)
A. Arbitrage with Two Currencies
B. Triangle Arbitrage (with Three Currencies)
3. Intertemporal Riskless Arbitrage (over Time)
A. Ruth’s Decision: Individual Optimization
B. Covered Interest Parity: Equilibrium Outcome
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3.A Ruth’s Decision
USD 1 Billion sales
revenue today
USD 1 Billion payment
to app developers
in three months
Suppose that Ruth only cares about the returns
in terms of the USD. She has two options.
A. Hold the $ deposit for 3 months at the Bank
of America in New York, or
Google CFO, Ruth Porat
B. Send $ to Paris and convert it into € now,
hold € deposit for 3 months,
then convert € deposit returns into $ and
send the money back to New York.
Euro
Bond/Deposit
15
3.A Ruth’s Decision
Available instruments in today’s markets:
• the dollar deposit pays a known return in dollars (𝒊$ = 𝟑. 𝟓% for 3 months), and
• the euro deposit pays a known return in euros (𝒊€ = 𝟑% for 3 months);
• the current spot rate is known (𝐄$/€ = 𝟏. 𝟐), but
• The spot rate in 3 months is unknown today. (exchange rate risk)
How can Ruth get ride of the exchange rate risk if she puts $1 billion
as the euro deposit for 3 months?
• Besides signing the spot contract to convert $ 1 billion into € today, Ruth also signs a forward
contract today to “lock in” the exchange rate (𝐅$/€ = 𝟏. 𝟐𝟏𝟐) for converting the euro deposit
returns into the USD in 3 months.
• The forward contract allows Ruth to hedge against the FX risk.
16
Quiz: Which option should Ruth take?
Interest rates and FX rates: 𝐄$/€ = 𝟏. 𝟐, 𝐅$/€ = 𝟏. 𝟐𝟏𝟐, 𝒊$ = 𝟑. 𝟓% and 𝒊€ = 𝟑%
Option A: hold $ deposits for 3 months => Ruth gets (1+ 𝒊$ )=1.035
billion US dollars.
?
Option B:
Today, Ruth
• coverts US$ 1 billion into
(The base currency?)
𝟏
𝐄$/€
=?
𝟎. 𝟖𝟑𝟑𝟑 billion euros and deposits them in Paris, and
• signs a 3-month forward contract of repurchasing the USD.
3 months later, Ruth
• gets the deposit return of
𝟏
𝑬$/€
(1+ 𝒊?
€ )=0.8583 billion euros and
• use the forward rate to convert the euro deposit return into
𝐅$/€
𝑬$/€
?
(1+ 𝒊€ ) ≈ $1.04 billion USD.
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Quiz: Which option should Ruth take?
In this case, (1+ 𝒊$ ) < (1+ 𝒊€ )
𝐅$/€
𝐄$/€
holds.
• Where should Ruth put the $ 1 billion? Euro deposits in Paris
• Can Ruth do better than this arrangement?
Buy low and sell high => borrow $ in NY and purchase euro deposit in Paris
• If all the FX traders behave like Ruth, how do the spot rate and the 3-month forward rate move
in the markets today?
 The rise in the demand for euro spot leads to a higher spot rate today 𝐄$/€ , and
 the rise in the supply of euro in 3 months => a fall in the 3-month forward rate today 𝐅$/€ .
• How do changes in FX rates affect the arbitrage opportunity as described by the inequality?
 The arbitrage opportunity triggers the individuals’ profit-seeking behaviors, while
 the latter eventually eliminate the arbitrage opportunity (“price gap”).
What if (1+ 𝒊$ ) > (1+ 𝒊€ )
𝐅$/€
𝐄$/€
holds?
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3.B Covered Interest Parity (CIP)
The Law of
One Price
in 3 months
Buy the BC (euro)
=> divide the
amount of
the QC by
the spot rate
Sell the BC (euro)
Compare with intratemporal
cross-market currency
arbitrage on page 9:
differences and similarities?
3 months ahead
=> multiply the
amount of the BC
by the pre-agreed
forward rate
in 3 months
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3.B Covered Interest Parity (CIP)
Similar as in the case of intratemporal currency arbitrage (page 9), the Law of One Price also
applies here but in a different format.
Covered Interest Parity (CIP):
(1+ 𝒊$ ) = (1+ 𝒊€ )
𝐅$/€
𝐄$/€
By signing a 3-month forward contract today,
• Ruth “locks in” the exchange rate for converting the € deposit return into $ three months later;
• whether/how the spot rate changes in the next 3 months is irrelevant for Google;
• all the exchange rate risk on the euro side has been “covered” by the forward contract.
Can you replace “covered” with another word?
Difference between hedging and speculation?
In equilibrium, the forward rate
is determined jointly by the two
interest rates and the spot rate, if
the conditions of the CIP are met.
𝐅$/€
(1+ 𝒊$ ) = (1+ 𝒊€ )
𝐄$/€
𝐅$/€ = 𝐄$/€
1+ 𝒊$
1+ 𝒊€
the CIP => the forward rate determination
20
Case Study: Test the CIP Theory with the Empirical Data
𝐅£/𝐃𝐌
(1+ 𝒊𝐃𝐌 )
− (1+ 𝒊£ )
𝐄£/𝐃𝐌
(Take the UK as the home country)
• In the 1970s, the difference was
positive and often large.
• Traders would have profited from
arbitrage by moving money from
British pound deposits to German
mark deposits, but capital
controls prevented them from
freely doing so.
Period of capital controls
Period of financial liberalization
• The excess return on German
mark deposits reflected the
limited arbitrage at that time.
• After financial liberalization around 1980, such profit opportunities essentially vanished, and the
CIP condition held, aside from small deviations due to transaction costs and measurement errors.
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A Summary of Learning Outcomes
Upon successful completion of module 2B, you should be able to:
• Understand the major instruments in the FX markets
o Distinguish between spot and forward contracts
o Use the ask/bid price to convert currencies correctly
• Intra-temporal arbitrage (with or without the ask-bid spread)
o Cross-market arbitrage
o Triangular arbitrage
• Riskless arbitrage over Time
o Use the forward contract to hedge against the FX risk
o The CIP is a result of riskless arbitrage, reflecting the Law of One Price over time.
1+ 𝒊$
o The CIP shows how the forward rate is determined in FX markets, 𝐅$/€ = 𝐄$/€
.
1+ 𝒊€
But, what determines the spot rate, 𝐄$/€ ? => Lecture 2C
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