International Finance
2024 November / December
Pr of Dr. Pr ab esh Lu itel
Lecturer
Prof. Prabesh Luitel
Office: L717
Email: p.luitel@ieseg.fr
Drop-in hours: Appointment by email
2
Reference textbooks (optional)
Eun C. & Resnick B., International Financial Management, McGraw-Hill
3
Other textbooks
4
Syllabus
•
Syllabus available from IESEGonline
Assessment methods
• final unseen exam: 2-hours length counting for 70% to be held (tentative date:
December 17th)
• continuous assessment: two sessions of MCQs of 15 mins each counting for 30%
(=15%+15%)
5
Course Outline
1. FOREX Markets
2. International Parity Relationships
3. Futures on FOREX
4. Options on FOREX
6
Your Duties
• Read the course materials BEFORE the course. If you don’t,
you are not going to profit from the sessions.
• Practice with the exercises available on IO.
• Ask all your questions during the course.
Your Rights
• To get access to high-quality knowledge and be able to compete:
• in a globalized labor market
• with more educated people around
• To ask questions and get answers to them
• To be “fairly” assess
• I am your coach and I am here to make:
• you succeed, not to make you fail;
• sure you reach an internationally recognized level of expertise.
Now, let us hit the road…
Any questions?
Contact your professor
What’s Special about “International” Finance?
• Foreign Exchange Risk and Political Risks
• Market Imperfections
• Expanded Opportunity Set
What’s Special about “International” Finance?
Foreign Exchange Risk
▪
This is risk that foreign currency profits may evaporate in local currency terms
due to unanticipated unfavorable exchange rate movements.
▪
▪
https://www.trade.gov/foreign-exchange-risk
https://www.youtube.com/watch?v=HqEIlpZ1_GE&t=88s
▪
Exchange rate risks remain a critical factor for companies
https://www.credit-suisse.com/ch/en/corporateclients/entrepreneurs/products/international-business/foreign-exchange/foreign-exchangemarket-2024-exchange-rate-risks-take-center-stage.html
11
What’s Special about “International” Finance?
Foreign Exchange Risk
FX Survey 2024. Assessment of exchange rate developments
https://www.credit-suisse.com/media/assets/privatebanking/docs/ch/unternehmen/unternehmen-unternehmer/publikationen/fx-study-2024-en.pdf
▪ Currency risk remains a primary concern, with around 40% of Swiss companies actively hedging.
Exporters hedge more frequently than importers or domestic-focused firms.
▪ Interest rate hedging remains low, with only 5% of companies using derivatives to mitigate rising
financing costs.
▪ Companies have varied hedging ratios based on industry, with service companies typically
hedging more than industrial firms due to different risk exposures.
12
What’s Special about “International” Finance?
Political Risk
• Sovereign governments have the right to regulate the movement of goods,
capital, and people across their borders.
• These laws sometimes change in unexpected ways.
• For e.g., changes in tax laws; expropriation of assets held by foreigners
• Sanctions can happen
Legal challenges of confiscating Russian central bank assets to support Ukraine
“In 2022, the EU, USA, Japan, and Canada froze approximately $300 billion in Russian sovereign assets. Around
$4-5 billion of these are under U.S. jurisdiction. G7 countries, the EU, and Australia have frozen €260 billion of
the Russian Federation's Central Bank assets. Most of these assets are stored in Euroclear, the central depository
registered in Belgium, mainly in securities, including European government bonds.” (Reuters, August 1, 2024)
Recent study on Political Risk
https://www.sciencedirect.com/science/article/abs/pii/S092911991500156X
https://www.sciencedirect.com/science/article/abs/pii/S0261560697000089
13
What’s Special about “International” Finance?
Market Imperfections
• Legal restrictions on the movement of goods, people, and money.
• Transactions costs : information asymmetry
• Excessive Shipping costs
• Tax arbitrage
What’s Special about “International” Finance?
Expanded Opportunity Set
• Firms can gain from greater economies of scale when their tangible
and intangible assets are deployed on a global basis.
• Locate where they can minimize the cost of production
• Access to global capital market
• Lower cost of capital
➢ For investors: large opportunity to diversify
Why Engage in International Transactions?
• The opportunity to internationally move people, money and material can
add value to firms that operate internationally (MNCs) and investors of
financial securities because:
- Can access multiple capital sources, thus lowering cost of capital for MNCs
- Can choose among different countries, thus reducing taxable income
- Can diversify portfolios of securities internationally
- Can diversify internationally sourcing, production and selling of products
• As a result, MNCs and international investors could reap higher returns
and less risky earnings than their domestic counterparts
17
https://en.wikipedia.org/wiki/List_of_circulating_currencies
18
What Types of Risks are Involved?
• The decision to go international brings following risks:
- Exposure to foreign exchange fluctuations (very difficult to predict)
- Exposure to political and macroeconomic risks of different countries
• To protect against such risks, MNCs and investors may participate in FX option,
forward and/or futures markets
Valuation of domestic firms
• The value of a firm is equal to net present value of stream of expected future
cash flows
• There are three basic elements for measuring value of a firm:
- The future streams of cash flows
- The required rate of return by the investors (ie rate used to discount future cash flows)
- The time period at which each cash flow is expected
Valuation of domestic firms
n
Value = 
t =1
E (CF$, t )
(1 + k )
t
E(CF$,t) = expected future cash flows to be received at the end of period t
n
= number of periods into the future in which cash flows are received
k
= required rate of return by investors (or cost of equity capital)
𝑁𝑒𝑡 𝑃𝑟𝑒𝑠𝑒𝑛𝑡 𝑉𝑎𝑙𝑢𝑒 = −𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 + 𝑃𝑟𝑒𝑠𝑒𝑛𝑡 𝑉𝑎𝑙𝑢𝑒
21
Valuation of MNCs
• A MNC’s financial decisions include:
- how much financing to obtain in each currency
- how much investment to direct in each currency
- how much business to conduct in each country
• Such decisions determine MNC exposure to international environment, since
its cash flows determined by exchange rate parities
• Eg Nissan’s financial decisions include
- raise funds (by taking loans or issuing new shares/bonds) in ¥, $, € and £
- use proceeds denominated in different currencies to build plants in UK/EU/US/JP
- target specific markets (say EU) so that large share of revenues denominated in €
(yet shareholders expect dividends paid in ¥)
Valuation of MNCs
m

E (CFj , t ) E (ER j , t ) 
n 
 j =1

Value =  

t
(1 + k )
t =1 





E(CFj,t) = expected cash flows denominated in currency j to be received by parent firm at the
end of period t
E(ERj,t) = expected exchange rate at which currency j can be converted into domestic currency
at the end of period t
k
= the weighted average cost of capital of parent company
23
Valuation of MNCs
Exposure to
Foreign Economies
Exchange Rate Risk
m

E (CFj , t ) E (ER j , t ) 
n 
 j =1

Value =  

t
(1 + k )
t =1 





• MNCs face exchange rate risk - ie the risk that foreign currency profits may
evaporate in domestic currency terms (eg ¥ for Nissan) due to unfavorable
exchange rate fluctuations
For financial investors
• Also investors face exchange rate risk - ie the risk that foreign currency profits
may evaporate once expressed in domestic currency due to unfavorable exchange
rate movements
• Example: Assume that you are a dollar-based investor, $1=¥100 and buy 10
shares of Toyota for ¥100,000 (i.e. $100 per share = ¥10,000 per share). One year
later the investment in shares has appreciated by 10% at ¥110,000
- as long as exchange rate $/¥ remains constant, your investment in US$ is now valued $???
- but, if the ¥ has depreciated to $1=¥120 then your initial investment of $1,000 is now
valued $???
25
For financial investors
• Also investors face exchange rate risk - ie the risk that foreign currency profits
may evaporate once expressed in domestic currency due to unfavorable exchange
rate movements
• Example: Assume that you are a dollar-based investor, $1=¥100 and buy 10
shares of Toyota for ¥100,000 (i.e. $100 per share = ¥10,000 per share). One year
later the investment in shares has appreciated by 10% at ¥110,000
- as long as exchange rate $/¥ remains constant, your investment in US$ is now valued
$1,100 (=110,000/100)
- but, if the ¥ has depreciated to $1=¥120 then your initial investment of $1,000 is now
valued $916.67 (=110,000/120)
26
Forecasting exchange rates
• To mitigate the effect of exchange rate risk MNCs and investors must be able to
predict future fluctuation in FX and master techniques to mitigate FX risk
- but exchange rate forecasting notoriously difficult
- more on this to follow
27
Monthly Japanese ¥/US$ Exchange Rate
Feb 1973: Bretton Woods
Agreement of fixed
exchange rates phased out
1973
• With repeal of Bretton Woods the prediction of FX became a big topic
• Read/click here for more details on “The End of Bretton Woods” CHAPTER 8 The
End of Bretton Woods? in: International Monetary Cooperation Since Bretton Woods (imf.org)
28
Daily US$/€ Exchange Rate
• FX fluctuate up and down on a daily basis as a result of market forces
Monthly € – Swiss Franc Exchange Rate
15th Jan 2015: Swiss National Bank
repeals the implicit Franc’s parity with
the Euro
Source: www.macrotrend.net
Press Release
(weblink)
Swiss National
Bank (SNB) - SNB
monetary policy
after the
discontinuation of
the minimum
exchange rate
• On top of market forces FX fluctuate as result of central banks’ decisions
Foreign Exchange Markets
Learning Objectives
• Understanding of function and structure of the FOREX Market
• Understand how to read market quotations
• Derive cross-rate quotations
• Triangular arbitrage
• Analyze FOREX forward market
• Define concept of forward premium
- Material for this lecture: Eun and Resnick, chapter 5
Function and Structure of FOREX Market
• FOREX markets make it possible conversion of purchasing power from one
currency into another, trading of foreign exchange options, forward and
futures contracts and currency swaps
• FOREX markets are over-the-counter (OTC) markets
- trading does not take place in a centralised marketplace (ie an exchange)
- rather the FOREX market is a worldwide network of bank currency traders, nonbank dealers and FX brokers connected one to another via electronic dealing systems
• Trading activities consist of speculative/arbitrage/hedging transactions
- speculative: attempts to correctly judge future price movements in one currency
versus another
- arbitrage: attempts to profit from temporary price discrepancies among currencies
- hedging: attempts to isolate from exchange rate risk
33
• FOREX market largest financial market in the world
- open 365 days a year, 24/7
- exchange rates constantly change, take a look!
• Main hubs of FOREX transactions are UK and US
https://www.reuters.com/markets/us/global-fx-trading-hits-record75-trln-day-bis-survey-2022-10-27/
➢Global FX trading volumes rise 14% to $7.5 trillion a day
➢Dollar retains market dominance, China's yuan sees biggest gain
London's share of trading dips post Brexit
➢80% of all FX trading takes place in the five FX trading hubs that are
major financial centres.
➢as the pre-eminent vehicle currency, the US dollar was on one side of
around 90% of all FX trades in April 2022
Global FX turnover
Read BIS paper here: https://www.bis.org/publ/qtrpdf/r_qt2212f.htm
35
Structure of FOREX Market
• FOREX made of commercial banks and foreign exchange brokers
- they trade in most of currencies
- they are connected continuously via e-platforms
• Participants in FOREX are
- individual and institutional investors, firms and MNCs: place buy/sell orders of
foreign currencies with commercial banks and/or brokers
Structure of the FX Market
Individuals
Individuals
MNCs
MNCs
Speculators
Speculators
Institutional Investors
Institutional Investors
37
Structure of FX Market
• FOREX made of commercial banks and foreign exchange brokers
- they trade in most of currencies
- they are connected continuously via e-platforms
• Participants in FOREX are
- individual and institutional investors, firms and MNCs: place buy/sell orders with
commercial banks and/or brokers
- commercial banks: carry out buy/sell orders on behalf of their clients by dealing
either directly with other banks (about 200 banks) or with brokers
- brokers: can often provide better quotation as they collect buy/sell orders from many
banks and for multiple currencies
38
Structure of the FX Market
Individuals
MNCs
Broker
Broker
Individuals
MNCs
Speculators
Institutional Investors
Local Bank
Local Bank
Speculators
Institutional Investors
39
Structure of the FX Market
Individuals
MNCs
Broker
Speculators
Local Bank
Major Banks
International Interbank
Market
Derivative
Markets
Broker
Individuals
MNCs
Institutional Investors
Local Bank
Speculators
Institutional Investors
40
Structure of FOREX Market
• FOREX made of commercial banks and foreign exchange brokers
- they trade in most of currencies
- they are connected continuously via e-platforms
• Participants in FOREX are
- individual and institutional investors, firms, MNCs and international investors: place
buy/sell orders with commercial banks
- commercial banks: carry out buy/sell orders from their clients by dealing either
directly with other banks (about 200 banks) or with brokers
- brokers: can often provide better quotation as they collect buy/sell orders from many
bank and for multiple currencies
- central banks: might intervene in FOREX by buying/selling national currency in order
to influence demand and supply and eventually market quotations
41
Structure of the FX Market
Individuals
MNCs
Broker
Speculators
Local Bank
Individuals
MNCs
Central
Banks
Major Banks
International Interbank
Market
Derivative
Markets
Broker
Institutional Investors
Local Bank
Speculators
Institutional Investors
42
Size of FX markets
OTC foreign exchange turnover
Net-net basis,1 daily averages in April, in billions of US dollars
Instrument
Foreign exchange instruments
2001
2004
Table 1
2007
2010
2013
2016
1,239
1,934
3,324
3,973
5,357
5,067
Spot transactions
386
631
1,005
1,489
2,047
1,652
Outright forwards
130
209
362
475
679
700
Foreign exchange swaps
656
954
1,714
1,759
2,240
2,378
7
21
31
43
54
82
60
119
212
207
337
254
1,381
1,884
3,123
3,667
4,917
5,067
12
25
77
145
145
115
Currency swaps
Options and other products²
Memo:
Turnover at April 2016 exchange rates 3
Exchange-traded derivatives 4
1
Ad ju sted f or local an d cross-b ord er in ter-d ealer d ou b le-cou n tin g (ie “ n et-n et” b asis). 2 T h e categ ory “ oth er FX p rod u cts” covers h ig h ly
leverag ed tran saction s an d /or trad es wh ose n otion al am ou n t is variab le an d wh ere a d ecom p osition in to in d ivid u al p lain van illa com p on en ts
was im p ractical or im p ossib le. 3 Non -US d ollar leg s of f oreig n cu rren cy tran saction s were con verted in to orig in al cu rren cy am ou n ts at
averag e exch an g e rates f or Ap ril of each su rvey year an d th en recon verted in to US d ollar am ou n ts at averag e Ap ril 2016 exch an g e rates.
4
Sou rces: Eu rom on ey T rad ed ata; Fu tu res In d u stry Association ; T h e Op tion s Clearin g Corp oration ; BIS d erivatives statistics. Foreig n
exch an g e f u tu res an d op tion s trad ed world wid e.
Source: http://www.bis.org/publ/rpfx13.htm
43
FX markets across the globe
44
FX markets across the globe and Trade Activity
The Spot Market
• Spot rate quotations can be direct or indirect
- Direct: how many dollars do I need to buy one unit of foreign currency? eg “British
Pounds is worth about 2 US dollars”
- Indirect: how many unit of foreign currency do I need to buy one dollar? eg “one US
dollar is worth about 0.5 British Pound”
• Notation used is the following
- S(j/k) is the price of one unit of currency k in term of j
- For instance S(£/$)=0.5 (indirect) and S($/£)=2 (direct)
Spot Rate Quotations
The direct quote for British pound
is £1 = $1.5627
Direct: how many dollars do I need
to buy one unit of foreign
currency (S($/£))?
Spot Rate Quotations
The indirect quote for British
pound is: £.6399 = $1
Indirect: how many units of GBP
do I need to buy one dollar
(S(£/$))?
Spot Rate Quotations
Note that the direct
quote is the
reciprocal of the
indirect quote as
1
1.5627 =
0.6399
49
Bid-Ask Spread
• The bid price is the price a dealer is willing to pay you for
something.
• The ask price is the amount a dealer wants you to pay for
something.
• It doesn’t matter if we’re talking used cars or used currencies: the
bid-ask spread is the difference between the bid and ask prices.
50
Bid-Ask Spread
• A dealer might offer:
• A bid price of $1.1250/€.
• An ask price of $1.1255/€.
• While there are a variety of ways to quote the above, the bid-ask spread
represents the dealer’s expected profit.
Ask − Bid
% spread =
× 100
Ask
$1.1255/€ − $1.1250/€
% spread = 0.444% =
× 100
$1.1255/€
51
Different Bid –Ask Spreads Estimators
• Effective Spreads
• Realized Spreads
• Corwin-Schultz Spreads
• Abdi Ranaldo Spreads
• Chung-Zhang Spreads
• Amihud Illiquidity
• Volume-based measure Liquidity
Check the pdf file in course page (Different estimators of Liquidity)
Each paper has some limitations, the common is that the estimated spreads are
generally negative, approximately 40% - 48% of estimated spreads of CS and AR are
negative which are set to Zero! A danger zone, where it introduces zero bias instead
of understanding the magnitude of that bias (irrespective of sign).
52
Cross Exchange Rates Quotations
Cross Exchange Rates Quotations
• Cross-rate is an exchange rate between a currency pair where neither currency is
the US $
- computed by making use of respective exchange rate against US $
• Suppose that S($/€) = 2 and S(¥/$) = 50
- i.e. €1 = 2 $ and $1 = ¥50
- then I would need ¥100 to buy €1
• More formally the €/¥ cross-rate can be computed as
€ € $
=  ,
¥ $ ¥
€0.5 $1 €0.5

=
 €1 = ¥100  S( € / ¥) = 0.01
$1 ¥50 ¥50
Exercises
Suppose you observe the following exchange rates: €1 = $1.25; £1 = $2.00. What must the
euro-pound exchange rate be?
a. €1 = £1.60
b. €1 = £0.625
c. €2.50 = £1
d. €1 = £2.50
55
Exercises
Suppose you observe the following exchange rates: €1 = $1.25; £1 = $2.00. What must the
euro-pound exchange rate be?
a. €1 = £1.60
Given above rates, with 1$ buy 0.8€.
b. €1 = £0.625
With 1$ buy 0.5£.
c. €2.50 = £1
Thus cross-rate must be 0.8/0.5=1.6€/£.
d. €1 = £2.50
Given cross-rate of 1.6€/£, with 1€ we can buy as much as
0.625£.
56
Exercises
Assume the Canadian dollar is equal to £0.50 and the Euro is equal to £1.2. The value of
the Euro in Canadian dollars is:
a. about 1.3231 Canadian dollars.
b. about 2.4 Canadian dollars.
c. about 2.136 Canadian dollars.
d. about 1.7951 Canadian dollars.
57
Exercises
Assume the Canadian dollar is equal to £0.50 and the Euro is equal to £1.2. The value of
the Euro in Canadian dollars is:
a. about 1.3231 Canadian dollars
b. about 2.4 Canadian dollars
c. about 2.136 Canadian dollars
d. about 1.7951 Canadian dollars
Given above rates, with 2CAN$ buy 1£.
With 1£ buy 0.833€.
So you need 2/0.833=2.400 CAN$ to buy 1 € .
58
Cross Ask and Bid Rates with Bid-Ask Spreads
USD Bank
Quotations
American Terms
European Terms
Bid
Ask
Bid
Ask
Pounds
1.2000
1.2500
.8000
.8333
Euros
1.0500
1.0510
.9515
.9524
€/£
???
???
???
???
Find the €/£ cross ask rate, consider a retail customer who starts
with €10,000, sells € for $, and buys £
Find the €/£ cross bid rate, consider a retail customer who starts
with £10,000, sells £ for $, and buys €
59
Cross Ask and Bid Rates with Bid-Ask Spreads
USD Bank
Quotations
American Terms
European Terms
Bid
Ask
Bid
Ask
Pounds
1.2000
1.2500
.8000
.8333
Euros
1.0500
1.0510
.9515
.9524
€/£
€1.1418
€1.1905
£0.8400
£0.8758
Find the €/£ cross ask rate, consider a retail customer who starts
with €10,000, sells € for $, and buys £
Find the €/£ cross bid rate, consider a retail customer who tarts
with £10,000, sells £ for $, and buys €
60
Cross Exchange Rates Quotations
• Cross-rate quotations convey the idea that once market delivers quotation for 2
currencies – say A and B - in terms of $ then exchange rate between A and B is
automatically determined
- call such exchange rate between A and B implied cross-rate
• Market forces will ensure that any departure of actual cross-rate from implied
rate is quickly absorbed
- Such market forces consist of triangular arbitrage
Triangular Arbitrage
• It is the process of trading out US dollars into a second currency, then trading it
for a third currency, which is in turn traded again for US dollars
- possible to earn arbitrage profits when direct exchange rates between second and third
currency is not aligned with implicit cross-rate!
Suppose we observe these
banks posting following
exchange rates
Cross-rate here is S(¥/£)=85
Are second and third
currency aligned to
implicit cross-rate?
First calculate the
implied cross rates to see
if an arbitrage exists
$
Credit Lyonnais buys $ and
sells £ @ S(£/$)=1.50
£
Barclays buys ¥ and sells $ @
S(¥/$)=120
Credit Agricole buys £
and sells ¥ @ S(¥/£)=85
¥
Triangular Arbitrage
The implied S(¥/£) cross rate
is S(¥/£) =120/1.5= 80
Yet Credit Agricole posted a quote
of S(¥/£)=85 so there is an
Credit Lyonnais buys $ and
arbitrage opportunity
$
sells £ @ S(£/$)=1.50
Credit Agricole pays more ¥
(actually 85¥) for 1£ than what
prescribed by market (80¥)!
£
Barclays buys ¥ and
sells $ @ S(¥/$)=120
Credit Agricole buys £
and sells ¥ @ S(¥/£)=85
¥
63
Triangular Arbitrage
• Assume you are initially endowed with US $. How can make profit?
$
1
Credit Lyonnais buys $ and
sells £ @ S(£/$)=1.50
1. Sell $ for £ to Credit Lyonnaise
2. Sell £ for ¥ to Credit Agricole
3
Barclays buys ¥ and sells $ @
S(¥/$)=120
2
£
Credit Agricole buys £
and sells ¥ @ S(¥/£)=85
¥
3. Sell ¥ for $ to Barclays
64
Triangular Arbitrage
• Assume you are initially endowed with $100,000:
1- Sell $100,000 buy £ from Credit Lyonnaise at S(£/$) = 1.5
=>
receive £150,000
2- Sell our £ 150,000 for ¥ to Credit Agricole at S(¥/£) = 85
=>
receive ¥12,750,000
3 - Sell ¥ 12,750,000 buy $ from Barclays at S(¥/$) = 120
=>
receive $106,250
• Profit per round trip = $ 106,250- $100,000 = $6,250
• Arbitrageurs can make risk-less profits but this cannot last forever!
65
Triangular Arbitrage
• As soon as possibility to make risk-less profits becomes of public domain
several arbitrageurs engage in same type of transaction
- Arbitrageurs all approach Credit Agricole to sell £ to buy ¥
- CA faces strong demand of ¥ against £ and start paying fewer ¥ for one £ (in other
words ¥ more expensive in terms of £)
- from initial 85¥ / 1£ the same 1£ will buy fewer ¥ (eg 0.845, 0.84, …, 0.81, …)
- when S(¥/£) = 80 no arbitrage opportunities available anymore
• Arbitrage opportunities quickly moped up in e-platforms through highfrequency trading (HFT)
- HFT algorithms scan FX markets in search of arbitrage opportunities to exploit
- this eliminates instantaneously any arbitrage opportunity
Exercises
Suppose you observe the following exchange rates: €1 = $.85; £1 = $1.60; and €2.00 = £1.00.
Compute the implied cross-rate €/£.
a. The implied cross-rate €/£ is €2.00=£1.00
b. The implied cross-rate €/£ is €1.8816=£1.00
c. The implied cross-rate €/£ is €1.9816 = £1.00
d. Not possible to compute the implied cross-rate €/£
Exercises
Suppose you observe the following exchange rates: €1 = $.85; £1 = $1.60; and €2.00 = £1.00.
Compute the implied cross-rate €/£.
a. The implied cross-rate €/£ is €2.00=£1.00
b. The implied cross-rate €/£ is €1.8816=£1.00
c. The implied cross-rate €/£ is €1.9816 = £1.00
d. Not possible to compute the implied cross-rate €/£
Given above rates, with 1$ buy 1.1764Eur.
With 1$ buy 0.625£.
So €/£ rate is 1.1764/0.625=1.882.
68
Exercises
Suppose you observe that Barclays buys £ for $ @ S($/£)=1.465, Credit Lyonnais buys $ for € @
S(€/$)=0.8171, and that Credit Agricole makes direct market £/€ by buying € for £ @
S(€/£)=1.191. How can you make arbitrage profits?
£
Barclays buys £ for $ @
S($/£)=1.465
Credit Agricole buys € for £ @
S(€/£)=1.191
$
€
Credit Lyonnais buys
$ for € @ S(€/$)=0.8171
69
Exercises
Suppose you observe that Barclays buys £ for $ @ S($/£)=1.465, Credit Lyonnais buys $ for € @
S(€/$)=0.8171, and that Credit Agricole makes direct market £/€ by buying € for £ @
S(€/£)=1.191. How can you make arbitrage profits?
Implicit cross-rate is S(€/£)= S($/£)× S(€/$)=
=1.465×0.8171=1.1971
Implicit cross-rate ≠1.191 so arbitrage possible
CA sells £ at 1.191 euros whereas
rate prescribed by market should
be more expensive at 1.1971
£
Barclays buys £ for $ @
S($/£)=1.465
Credit Agricole buys € for £ @
S(€/£)=1.191
$
€
Credit Lyonnais buys
$ for € @ S(€/$)=0.8171
70
Exercises
Suppose you observe that Barclays buys £ for $ @ S($/£)=1.465, Credit Lyonnais buys $ for € @
S(€/$)=0.8171, and that Credit Agricole makes direct market £/€ by buying € for £ @
S(€/£)=1.191. How can you make arbitrage profits?
Sell $5,000,000 to Credit Lyonnais to get
$5,000,000×0.8171= € 4,085,500
£
$
€
Credit Lyonnais buys
$ for € @ S(€/$)=0.8171
71
Exercises
Suppose you observe that Barclays buys £ for $ @ S($/£)=1.465, Credit Lyonnais buys $ for € @
S(€/$)=0.8171, and that Credit Agricole makes direct market £/€ by buying € for £ @
S(€/£)=1.191. How can you make arbitrage profits?
Sell $5,000,000 to Credit Lyonnais to get
$5,000,000×0.8171= €4,085,500
Sell € 4,085,500 to Credit Agricole to get
€ 4,085,500/1.191= £3,430,311 (pay less
Euro 1.191 vs 1.1971to buy GBP)
£
Credit Agricole buys € for £ @
S(€/£)=1.191
$
€
Credit Lyonnais buys
$ for € @ S(€/$)=0.8171
72
Exercises
Suppose you observe that Barclays buys £ for $ @ S($/£)=1.465, Credit Lyonnais buys $ for € @
S(€/$)=0.8171, and that Credit Agricole makes direct market £/€ by buying € for £ @
S(€/£)=1.191. How can you make arbitrage profits?
Sell $5,000,000 to Credit Lyonnais to get
$5,000,000×0.8171= €4,085,500
Sell € 4,085,500 to Credit Agricole to get
€ 4,085,500/1.191= £3,430,311 (pay lessBarclays buys £ for $ @
Euro 1.191 vs 1.1971to buy GBP)
S($/£)=1.465
£
Sell £3,430,311 to Barclays to get
£3,430,311×1.465=USD5,025,406
Credit Agricole buys € for £ @
S(€/£)=1.191
$
€
Credit Lyonnais buys
$ for € @ S(€/$)=0.8171
73
Cross Exchange Rates Quotations
• Market forces will ensure that any departure of actual (quoted) cross-rate from
implied rate is quickly absorbed
• In technical gergeon we say that FX market – through the computation of the
implied cross-rates – enforces discipline on market participants so that they
cannot set up quoted cross-rates that depart from the implied ones
Exercises
Suppose you observe the following exchange rates: €1 = $.85; £1 = $1.60; and €2.00 = £1.00.
Starting with $1,000,000, how can you make arbitrage profits?
a. Exchange $1m for £625,000 at £1 = $1.60. Buy €1,250,000 at €2 = £1.00; trade for
$1,062,500 at €1 = $.85.
b. Start with dollars, exchange for euros at €1 = $.85; exchange for pounds at €2.00 = £1.00;
exchange for dollars at £1 = $1.60.
c. Start with euros; exchange for pounds; exchange for dollars; exchange for euros
d. None of the above.
75
Exercises
Suppose you observe the following exchange rates: €1 = $.85; £1 = $1.60; and €2.00 = £1.00.
Starting with $1,000,000, how can you make arbitrage profits?
a. Exchange $1m for £625,000 at £1 = $1.60. Buy €1,250,000 at €2 = £1.00; trade for
$1,062,500 at €1 = $.85.
b. Start with dollars, exchange for euros at €1 = $.85; exchange for pounds at €2.00 = £1.00;
exchange for dollars at £1 = $1.60.
c. Start with euros; exchange for pounds; exchange for dollars; exchange for euros
d. None of the above.
Given above rates you get 1.1764 €=1$ and 0.625 £=1$, so S(€/£)=1.1764/0.625=1.8822 ie
1.8822€=1£. Thus implicit cross rate S(€/£) different from €2.00 = £1.00. Can sell £ in
exchange of € and get 2€ instead of 1.8822€. So start with $, sell $ for £, then sell £ for € (at
rate €2.00 = £1.00), then sell € for $.
76
Exercises
Consider again the above exercise where you observe the following exchange rates: €1 = $.85;
£1 = $1.60; and €2.00 = £1.00. The arbitrage profits are eliminated because arbitrageurs:
a. Sell £ and buy € in large quantities so that the GBP loses value against the Euro
b. Buy £ and sell € in large quantities so that the GBP loses value against the Euro
c. Buy £ and sell € in large quantities so that the Euro loses value against the GBP
d. Sell £ and buy € in large quantities so that the Euro loses value against the GBP
77
Exercises
Consider again the above exercise where you observe the following exchange rates: €1 = $.85;
£1 = $1.60; and €2.00 = £1.00. The arbitrage profits are eliminated because arbitrageurs:
a. Sell £ and buy € in large quantities so that the GBP loses value against the Euro
b. Buy £ and sell € in large quantities so that the GBP loses value against the Euro
c. Buy £ and sell € in large quantities so that the Euro loses value against the GBP
d. Sell £ and buy € in large quantities so that the Euro loses value against the GBP
78
Exercises
Suppose you observe the following exchange rates: €1 = $.85; £1 = $1.60; and €1.882 = £1.00.
Starting with $1,000,000, how can you make arbitrage profits?
a. Exchange $1m for £625,000 at £1 = $1.60. Buy €1,250,000 at €2 = £1.00; trade for
$1,062,500 at €1 = $.85.
b. Start with dollars, exchange for euros at €1 = $.85; exchange for pounds at €2.00 = £1.00;
exchange for dollars at £1 = $1.60.
c. Start with euros; exchange for pounds; exchange for dollars; exchange for euros
d. It is not possible to make arbitrage profits.
79
Exercises
Suppose you observe the following exchange rates: €1 = $.85; £1 = $1.60; and €1.882 = £1.00.
Starting with $1,000,000, how can you make arbitrage profits?
a. Exchange $1m for £625,000 at £1 = $1.60. Buy €1,250,000 at €2 = £1.00; trade for
$1,062,500 at €1 = $.85.
b. Start with dollars, exchange for euros at €1 = $.85; exchange for pounds at €2.00 = £1.00;
exchange for dollars at £1 = $1.60.
c. Start with euros; exchange for pounds; exchange for dollars; exchange for euros
d. It is not possible to make arbitrage profits.
Given above rates you get 1.1764 €=1$ and 0.625 £=1$, so S(€/£)=1.1764/0.625=1.8822 ie
1.8822€=1£. Thus, implicit cross-rate S(€/£) is equal to quoted rate €1.882 = £1.00. In this
case it is not possible to make arbitrage profits.
80
Forward Exchange Rates
(Can we secure a rate for a future date?)
The Forward Market
• A forward contract is an agreement to buy or sell an asset in the future at prices
agreed upon today
- eg if you ever have ordered an out-of-stock book then you have signed a forward contract in
which you agreed to buy an asset (book) in the future at a price negotiated today
• Forward FX contracts involves agreements to buy or sell foreign currencies in the
future at prices agreed upon today
- quotes for 1-, 3-, 6-, 9- and 12-month maturities available for forward contracts
- forward rates usually differ from spot rate: can be higher (at premium) or lower (at discount)
• Forward contracts are over-the-counter (OTC) products
- they are specifically tailored on the needs of two counterparties signing contracts
- unlike futures contracts which carry pre-specified features (more to come in next topic !)
82
Non Deliverable Forward Contract
• Due to government-initiated capital controls, the currencies of
some emerging market countries not freely traded.
• For many of these currencies, trading in non-deliverable forward
contracts exists.
• A non-deliverable forward contract is settled in cash, usually U.S.
dollars.
• Settlement is calculated by the difference between the forward price
agreed to in the contract and the spot price at maturity of the contract
multiplied by the contract size.
• You can read about Chinese Yuan NDF here
https://www.bochk.com/images/upload/retail/pdf/NDF_en.pdf
83
Forward Rate Quotations
• Consider spot and 180-day forward rates for British Pound (GBP)
- spot rate is $1.5627 = £1.00
- while 180-day forward rate (as of today) is $1.5445 = £1.00
• Can secure today rate of $1.5445=£1 six months ahead by buying 180-day forward
• Forward rate is at discount since 1.5445<1.5627
- it means that financial markets expect GBP to be worth less (in terms of US$) in six
months!
- can say that markets expect GBP to depreciate – ie it will cost fewer dollars to buy 1
GBP in 180 days
• Forward rates can be used to make a guess of what spot rates will be t months
ahead into the future
▪ Forward rate is an unbiased predictor of the expected spot rate under an assumption of
84
risk-neutrality
Forward Rate Quotations
Market participants expect that
the pound will be worth less in
dollars in 1, 3 and 6 months
into the future.
Forward Rate Quotations
Market participants expect that
the US$ will be worth more in
terms of GBP in 1, 3 and 6
months into the future.
Forward Premium
• Forward Premium (or discount) is spread between spot and forward rates at
maturities 1, 3, 6 and 12 month
• Useful to have an understanding of how much exchange rates will
appreciate/depreciate in near future
• For example, given that S($/£)=1.5627, F180($/£)=1.5445 the forward premium
given by:
F180 ($ / £) − S ($ / £) 360 1.5445 − 1.5627
f180,$ / £ =

=
 2 = −0.0233
S ($ / £)
180
1.5627
• We say that GBP is trading at 2.33% discount versus US $ for delivery in 180 days
87
Exercises
The forward rate is the exchange rate used for immediate exchange of currencies.
a. true.
b. false.
88
Exercises
The forward rate is the exchange rate used for immediate exchange of currencies.
a. true
b. false
89
Exercises
The spot and forward foreign exchange market:
a. Is an over-the-counter market.
b. Is open 24 hours a day, 7 days a week, somewhere in the world.
c. Is the largest and most active financial market in the world.
d. All of the above.
90
Exercises
The spot and forward foreign exchange market:
a. Is an over-the-counter market.
b. Is open 24 hours a day, 7 days a week, somewhere in the world.
c. Is the largest and most active financial market in the world.
d. All of the above.
91
Exercises
Consider the following spot and forward rate quotations:
S($/€)=0.85
F1($/€)=0.86
F2($/€)=0.87
F3($/€)=0.88
Which of the following is true:
a. The euro is definitely going to be worth more dollars in six months.
b. The euro is probably going to be worth less in dollars in six months
c. The euro is trading at a forward discount.
d. The euro is trading at a forward premium.
92
Exercises
Consider the following spot and forward rate quotations:
S($/€)=0.85
F1($/€)=0.86
F2($/€)=0.87
F3($/€)=0.88
Which of the following is true:
a. The euro is definitely going to be worth more dollars in six months.
b. The euro is probably going to be worth less in dollars in six months
c. The euro is trading at a forward discount.
d. The euro is trading at a forward premium.
93
Exercises
Consider the following spot and forward rate quotations:
S($/€)=0.85
F1($/€)=0.86
F2($/€)=0.87
F3($/€)=0.88
Calculate the three-month forward premium (assume 30-day months and 360-day years).
a. 3.53%
b. 0.4235
c. 0.1364
d. 0.1412
94
Exercises
Consider the following spot and forward rate quotations:
S($/€)=0.85
F1($/€)=0.86
F2($/€)=0.87
F3($/€)=0.88
Calculate the three-month forward premium (assume 30-day months and 360-day years).
a. 3.53%
b. 0.4235
c. 0.1364
d. 0.1412[=((0.88-0.85)/0.85)×360/90]
95
Exercises
Consider the following spot and forward rate direct and indirect quotations:
S($/€)=1.2238
S(€/$)=0.8171
F3($/€)=1.2251
F3(€/$)=0.8163
Calculate the three-month direct and indirect forward premium (assume 30-day months
and 360-day years)
a. 0.0042 and -0.0039
b. -0.0042 and 0.0039
c. 0.0042 and -0.0042
d. 0.0039 and -0.0039
96
Exercises
Consider the following spot and forward rate direct and indirect quotations:
S($/€)=1.2238
S(€/$)=0.8171
F3($/€)=1.2251
F3(€/$)=0.8163
Calculate the three-month direct and indirect forward premium (assume 30-day months
and 360-day years)
a. 0.0042 and -0.0039 [=[(1.2251-1.2238)/1.2238]×360/90]
b. -0.0042 and 0.0039
c. 0.0042 and -0.0042
d. 0.0039 and -0.0039
97
Exercises
Consider the following spot and forward quotations between the US$ and the
British Pound: S($/£)=1.5627 and F180($/£)=1.5445. Which of the following is
true:
a. The forward premium is -0.0233.
b. The British Pound is trading at discount.
c. There is a probability that the British Pound will depreciate in the coming six
months.
d. All of the above answers are correct.
98
Exercises
Consider the following spot and forward quotations between the US$ and the
British Pound: S($/£)=1.5627 and F180($/£)=1.5445. Which of the following is
true:
a. The forward premium is -0.0233.
b. The British Pound is trading at discount.
c. There is a probability that the British Pound will depreciate in the coming six
months.
d. All of the above answers are correct.
[(1.5445 – 1.5627)/1.5627]x(360/180)=-0.0233
99
Long and Short Forward Positions
• If you agree to sell anything (spot or forward) then you are “short”
- If you agree to sell given currency forward in t-month time then you are short
• If you agree to buy anything (forward or spot) then you are “long”
- If you agree to buy given currency forward in t-month time then you are long
• If one enters forward contracts then she locks in the forward price for future
purchase/sale of foreign currencies
- regardless the level of spot price at maturity, the trader must buy (if long) or sell (if
short) at the price agreed in the forward contract
- difference between spot price at maturity and price agreed in forward contract
determines profit or loss of long and short positions
- If long position makes profit then short makes equivalent losses, and vice versa
- Forward contracts can also be used for speculative purpose
Payoff Profiles (short position)
• Assume you sell Swiss Francs (SF) and price agreed in forward contract is
F90($/SF) = .8517 while S90($/SF) is spot rate 90 days ahead and you expect US $ to
appreciate against SF over next 3 month (will take fewer $ to buy 1SF)
Short position
profit
0
If you agree to sell anything in the future at a set price and the spot price later
falls - ie SF will cost less dollars (US$ appreciates as it takes fewer $ to buy
the same 1SF) - then you gain. In fact, to honor forward contract you must buy
SF in spot market at price < $0.8517 and then deliver SF at $0.8517
S90($/SF)
F90($/SF) = .8517
45°
loss
Price of 1SF in US$
agreed in forward contract
Payoff Profiles (short position)
• Assume you sell SF and price agreed in forward contract is F90($/SF) = .8517
while S90($/SF) is spot rate 90 days ahead and you expect US $ to appreciate
against SF over next 3 month (will take fewer $ to buy 1SF)
Short position
profit
0
S90($/SF)
F90($/SF) = .8517
If you agree to sell anything in the future at a set price and the spot price later rises - ie the SF will cost
more dollars (US$ depreciates) - then you make losses. In fact, to honor forward contract you have to buy
loss SF in spot market at price > $0.8517 and then deliver SF at $0.8517.
102
Payoff Profiles (short position)
• Assume you expect US$ to appreciate against Swiss Franc (ie it will take fewer $
to buy one SF) over next 3 month
• Potential profit if you lock in a short position
Short position
profit
If S90($/SF) = 0.8447 (therefore your prediction was right) trader must
buy SF in spot market at the price $0.8447 and deliver (sell) them under
forward contract at the price $0.8517 making a profit of ($0.8517 $0.8447) = $0.0070
.0070
S90($/SF)
0
.8447
F90($/SF) = .8517
loss
103
Payoff Profiles (short position)
• If you expect US $ to appreciate against Swiss Franc (SF) over next 3 month but
your expectations turn out to be wrong (so that it will take more than 0.8517$ to
buy one SF) then potential loss if you lock in a short position
Short position
profit
If S90($/SF) = 0.8447 (therefore your prediction was right) trader must
buy SF in spot market at the price $0.8447 and deliver (sell) them under
forward contract at the price $0.8517 making a profit of ($0.8517 $0.8447) = $0.0070
.0070
S90($/SF)
0
.8447
F90($/SF) = .8517
.8547
-.0030
loss
If instead S90($/SF) = 0.8547 (therefore your prediction was wrong) trader must buy SF in
spot market at the price $0.8547 and deliver (sell) them under the forward contract at the
price $0.8517, making a loss of ($0.8517 - $0.8547) = -$0.0030
104
Payoff Profiles (long position)
• Assume you expect US $ to depreciate against Swiss Franc (SF) over next 3
month (so that it will take more than 0.8517$ to buy one SF)
• You agree to buy SF at price $0.8517 in 90 days
Long position
profit
If you agree to buy anything in the future at a set price and the spot price later
rises then you gain. In fact, you are committed to buy SF at $0.8517 and then can
sell SF in spot market at price > $0.8517
0
F90($/SF) = .8517
45°
loss
S90($/SF)
Payoff Profiles (long position)
• Assume you expect US $ to depreciate against Swiss Franc (SF) over next 3
month
• You agree to buy SF at price $0.8517 in 90 days
Long position
profit
0
F90($/SF) = .8517
loss
S90($/SF)
If you agree to buy anything in the future at a set price and the spot price later falls then
you make a loss. In fact, you are committed to buy SF at $0.8517 and then can sell
SF in spot market but at price < $0.8517
106
Payoff Profiles (long position)
• Assume you expect US $ to depreciate against Swiss Franc (SF) over next 3
month
• Potential profit if you lock in a long position
Long position
profit
.0030
If S90($/SF) = 0.8547 (therefore your prediction was right) trader must buy SF under the
forward contract at the price $0.8517 and can then sell in spot market at the price $0.8547,
making a profit of ($0.8547-$0.8517) = $0.0030
0
F90($/SF) = .8517
.8547
S90($/SF)
loss
107
Payoff Profiles (long position)
• Assume you expect US $ to appreciate against Swiss Franc (SF) over next 3
month but your expectations turn out to be wrong
• Potential loss if you lock in a long position
Long position
profit
.0030
0
If S90($/SF) = 0.8547 (therefore your prediction was right) trader must buy SF under the
forward contract at the price $0.8517 and can then sell in spot market at the price $0.8547,
making a profit of ($0.8547-$0.8517) = $0.0030
.8447
F90($/SF) = .8517
.8547
S90($/SF)
If S90($/SF) = 0.8447 (therefore your prediction was wrong) trader must buy SF
-.0070
under the forward contract at agreed price $0.8517 and can then sell in spot market
loss
at the price $0.8447, making a loss of ($0.8447 - $0.8517) = -$0.0070
108
Payoff Profiles (long vs short positions)
• Assume you expect US $ to depreciate against SF over next 3 month whereas
Paul expect US$ to appreciate
• Both you (long) and Paul (short) agree to enter forward contract with F90($/SF)
= .8517 profit
0
F90($/SF) = .8517
S90($/SF)
loss
109
Payoff Profiles (long vs short positions)
• Assume you expect US $ to depreciate against SF over next 3 month whereas
Paul expect US$ to appreciate
• Both you (long) and Paul (short) agree to enter forward contract with F90($/SF)
= .8517 profit
You expect S90($/SF) to be greater than 0.8517
0
F90($/SF) = .8517
S90($/SF)
loss
110
Payoff Profiles (long vs short positions)
• Assume you expect US $ to depreciate against SF over next 3 month so enter a
long position whereas Paul expect US$ to appreciate so he goes short
• Both you (long) and Paul (short) agree to lock-in forward contract with F90($/SF)
= .8517 profit
Paul expects S90($/SF) to be lower than 0.8517
0
F90($/SF) = .8517
S90($/SF)
loss
111
Payoff Profiles (long vs short positions)
• Assume you expect US $ to depreciate against SF over next 3 month whereas
Long position
Paul expect US$ to appreciate
• Both you (long) and Paul (short) agree to enter forward contract with F90($/SF)
S90($/SF) = 0.8547 (therefore you were right and Paul was wrong) then you (holder of long
= .8517 profit Ifposition)
must buy SF under the forward contract at the price $0.8517 from Paul and can then sell
.0030
in spot market at the price $0.8547 making a profit of ($0.8547-$0.8517) = $0.0030
0
F90($/SF) = .8517
.8547
S90($/SF)
loss
112
Payoff Profiles (long vs short positions)
• Assume you expect US $ to depreciate against SF over next 3 month whereas
Long position
Paul expect US$ to appreciate
• Both you (long) and Paul (short) agree to enter forward contract with F90($/SF)
If S90($/SF) = 0.8547 Paul (holder of short position) must sell SF to you
= .8517 profit
.0030
under forward contract at agreed price $0.8517 whereas it could have sold in spot
market at the price $0.8547, making a loss of ($0.8517 - $0.8547) = -$0.0030
0
F90($/SF) = .8517
.8547
S90($/SF)
-.0030
You make $0.0030 for each SF you buy
loss
whereas Paul loses $0.0030 for each SF
he sells
Exercises
Consider a trader who takes a long position in a six-month forward contract on British
pounds. The forward rate is $1.75 = £1.00; the contract size is £62,500. At the maturity of the
contract the spot exchange rate is $1.65 = £1.00
a. The trader has lost $625.
b. The trader has lost $6,250.
c. The trader has made $6,250.
d. The trader has lost $66,287.88
114
Exercises
Consider a trader who takes a long position in a six-month forward contract on British
pounds. The forward rate is $1.75 = £1.00; the contract size is £62,500. At the maturity of the
contract the spot exchange rate is $1.65 = £1.00
a. The trader has lost $625.
b. The trader has lost $6,250. [(1.65-1.75)x62,500=-6,250]
c. The trader has made $6,250.
d. The trader has lost $66,287.88
115
Exercises
Consider a trader who takes a short position in a six-month forward contract on British
pounds. The forward rate is $1.75 = £1.00; the contract size is £62,500. At the maturity of the
contract the spot exchange rate is $1.65 = £1.00
a. The trader has lost $625.
b. The trader has lost $6,250.
c. The trader has made $6,250.
d. The trader has lost $66,287.88
116
Exercises
Consider a trader who takes a short position in a six-month forward contract on British
pounds. The forward rate is $1.75 = £1.00; the contract size is £62,500. At the maturity of the
contract the spot exchange rate is $1.65 = £1.00
a. The trader has lost $625.
b. The trader has lost $6,250.
c. The trader has made $6,250. [(1.75-1.65)x62,500=6,250]
d. The trader has lost $66,287.88
117
Exercises
The current spot exchange rate is $1.15/€ and the three-month forward rate is $1.25/€. Based
upon your crystal ball, you are pretty confident that the spot exchange rate will be $1.00/€ in
three months. Assume that you would like to buy or sell €100,000. What actions would you take
to speculate in the forward market? How much will you make if your prediction is correct?
a. Take a short position in a forward. If you’re right you will make $15,000
b. Take a long position in a forward contract on €100,000. If you’re right you will make $25,000
c. Take a short position in a forward contract on €100,000. If you’re right you will make $25,000
d. Take a long position in a forward contract on €100,000. If you’re right you will make $15,000
118
Exercises
The current spot exchange rate is $1.15/€ and the three-month forward rate is $1.25/€. Based
upon your crystal ball, you are pretty confident that the spot exchange rate will be $1.00/€ in
three months. Assume that you would like to buy or sell €100,000. What actions would you take
to speculate in the forward market? How much will you make if your prediction is correct?
a. Take a short position in a forward. If you’re right you will make $15,000
b. Take a long position in a forward contract on €100,000. If you’re right you will make $25,000
c. Take a short position in a forward contract on €100,000. If you’re right you will make $25,000
d. Take a long position in a forward contract on €100,000. If you’re right you will make $15,000
119
Exercises
Assume that three-month forward rate $/SF is $0.8686/SF and that based upon your crystal ball
you are confident that the spot exchange rate will be $0.8616/SF in three months. Assume that
you would like to buy or sell SF5,000,000. What actions would you take to speculate in the
forward market? How much will you make if your prediction is correct?
a. Take a short position forward. If you’re right you can buy at SF at 0.8616$ and sell at 0.8686$
b. Take a long position forward. If you’re right you will make (0.8686-0.8616)×5,000,000
c. Take a short position forward. If you’re right you can buy at SF at 0.8686$ and sell at 0.8616$
d. None of the above.
Exercises
Assume that three-month forward rate $/SF is $0.8686/SF and that based upon your crystal ball
you are confident that the spot exchange rate will be $0.8616/SF in three months. Assume that
you would like to buy or sell SF5,000,000. What actions would you take to speculate in the
forward market? How much will you make if your prediction is correct?
a. Take a short position forward. If you’re right you can buy at SF at 0.8616$ and sell at 0.8686$
b. Take a long position forward. If you’re right you will make (0.8686-0.8616)×5,000,000
c. Take a short position forward. If you’re right you can buy at SF at 0.8686$ and sell at 0.8616$
d. None of the above.
International Parity Relationships
Learning Objectives:
- Interest Rate Parity (IRP)
- Purchasing Power Parity (PPP)
- Covered Interest Arbitrage
- The Fisher Effect (FE)
- The International Fisher Effect (IFE)
- Forward Expectations Parity (FEP)
Material can be found in Eun and Resnick, chapter 6
Interest Rate Parity (IRP)
• IRP is a no arbitrage condition
• Arbitrage implies buying an asset in one market and simultaneously selling a
virtually identical asset in another market at higher price
- arbitrage is risk-free
• If IRP doesn’t hold then there are arbitrage opportunities and possible to
make unlimited risk-less profits
• Since we don’t typically observe persistent arbitrage conditions, we can safely
assume that IRP holds
•
•
Interest Rate Parity
S($/£) and F($/£) represent dollar price of one unit of pound on spot and
forward markets
Assuming you are investing in risk free instruments, suppose you have $1
to invest for one year. You can either
1 - invest in US at i$ to obtain future value = $1(1 + i$)
or
2a - trade your dollar for pounds at the spot rate and obtain $1(1/S) pounds, or
simply (1/S) pounds
- invest pounds in UK at i£ with maturity value of (1/S)(1+ i£ )
2b - sell maturity value of UK investment forward in exchange of a pre-determined
dollar amount (i.e. hedge your exchange rate risk by selling the future value of the
UK investment forward). The future value in $ is = (1/S)(1 + i£ )F
So the effective dollar interest rate from the UK investment is = (F/S)(1 + i£ ) - 1
Interest Rate Parity
•
•
Investment in US is riskless since the amount of US $ you will receive in
one year is known today
Investment in UK affected by exchange rate risk (you do not know what
level the exchange rate will be in one year)
- however, exchange rate risk eliminated by buying today forward contract (ie by
locking in forward rate)
•
Thanks to forward contract also amount of US $ you will receive in one year
from UK investment is known (certain) today
- therefore also UK investment is riskless
•
If both investments have same risk (both are risk less actually) then they
must have same future value—otherwise an arbitrage would exist
- therefore (F/S)(1 + i£) = (1 + i$)
Interest Rate Parity
• Formally
(F/S)(1 + i£) = (1 + i$)
or
1 + i$
1 + i£
F
=
S
IRP is sometimes approximated as
i$ – i£
1 + 𝑖$
F=S
1 + 𝑖£
=
F–S
S
Forward exchange rate will deviate from Spot
rate as long as the interest rates of the two
countries are not same!
This is forward premium
(discount). Remember that?
Interest Rate Parity
• IRP became popular through the writings of J. M. Keynes
John Maynard Keynes
1883-1946
Interest Rate Parity
•
•
IRP provides linkage between interest rates in two different countries via
forward premium
Assume GBP at forward premium (US$ at forward discount) i.e. F>S
- this implies that US $ expected to depreciate (GBP expected to appreciate) in future
- if so, US interest rate i$ should be higher to compensate expected depreciation of US $
- otherwise nobody would hold dollar-denominated securities
•
Vice-versa if GBP at forward discount (US$ is at premium) i.e. F<S
- US interest rate i$ should be lower than UK rate i£
- otherwise nobody would hold pound-denominated securities
•
When IRP holds, investors are indifferent between investing in US or
investing in UK with forward hedging
IRP and Covered Interest Arbitrage
• If IRP doesn’t hold then arbitrage opportunities exist
• IRP ensures that the difference in interest rates between two countries is offset
by the forward exchange rate, thereby preventing arbitrage profits.
𝐹
1 + 𝑖$
=
𝑆 1 + 𝑖𝐺𝐵𝑃
• Covered Interest Arbitrage exploits deviations from IRP, but such opportunities
are typically short-lived due to the actions of arbitrageurs.
• If IRP does not hold, then:
• You would prefer to invest where you will be better off.
• Invest in US if 1 + 𝑖$ is greater than (F/S)(1 + i£)
• Invest in UK if 1 + 𝑖$ is less than (F/S)(1 + i£)
IRP and Covered Interest Arbitrage
• If IRP doesn’t hold then arbitrage opportunities exist
• Consider the following set of foreign and domestic interest rates and spot and
forward exchange rates and check if IRP holds?
Spot exchange rate
S($/£) = $1.25/£
360-day forward rate
F360($/£) = $1.20/£
U.S. interest rate
i$ = 7.10%
British interest rate
i£ = 11.56%
IRP and Covered Interest Arbitrage
• If IRP doesn’t hold then arbitrage opportunities exist
• Consider the following set of foreign and domestic interest rates and spot and
forward exchange rates and check if IRP holds?
Spot exchange rate
S($/£) = $1.25/£
360-day forward rate
F360($/£) = $1.20/£
U.S. interest rate
i$ = 7.10%
British interest rate
i£ = 11.56%
𝐹
1 + 𝑖$
=
𝑆 1 + 𝑖𝐺𝐵𝑃
1.2
1 + 0.071
=
1.25 1 + 0.1156
IRP and Covered Interest Arbitrage
• A trader with $1,000 could invest in US so that in one year investment will be
worth $1,000(1+ i$) = $1,000(1.071) =$1,071
• Alternatively, this trader could exchange $1,000 for £800 at the prevailing spot
rate (£800=$1,000 or $1.25/£)
• Invest £800 at i£ = 11.56% for one year to achieve £892.48
• Then convert £892.48 back into dollars at F360($/£) = $1.20/£
• The £892.48 will be exactly $1,071
• In this case IRP holds and no arbitrage opportunities arise (impossible to make
risk-less profits)
Exercises
Suppose one-year interest rates in the US are 5% when the spot exchange rate is $0.75 = €1 and
the interest rate in France is 8% per year. What must the one-year forward exchange rate be?
a. $0.7292 = €1
b. $0.75 = €1
c. $0.81 = €1
d. $0.7714 = €1
Exercises
Suppose the one-year interest rates in the US are 5% when the spot exchange rate is $0.75 = €1
and the interest rate in France is 8% per year. What must the one-year forward exchange rate be?
𝐹
1 + 0.05
a. $0.7292 = €1
=
b. $0.75 = €1
c. $0.81 = €1
d. $0.7714 = €1
0.75
1 + 0.08
Exercises
Suppose that the spot exchange rate for Japanese yen is ¥122/$ and that the one year forward
exchange rate for Japanese yen is ¥130/$. The one-year interest rate is 5% in the U.S. What's the
interest rate in Japan?
a. 6.56%
b. 11.89%
c. 3.28%
d. 1.67%
136
Exercises
Suppose that the spot exchange rate for Japanese yen is ¥122/$ and that the one year forward
exchange rate for Japanese yen is ¥130/$. The one-year interest rate is 5% in the U.S. What's the
interest rate in Japan?
a. 6.56%
b. 11.89%
c. 3.28%
d. 1.67%
1 + 𝑖𝐽𝑃
130
=
122 1 + 0.05
137
Exercises
Suppose that the 1-year interest rate in the US is 5%, the spot exchange rate is $0.75 = €1 and
the 1-year forward rate is $0.75 = €1. What must the one-year interest rate in France if the IRP
between France and the US holds?
a. 5%.
b. 6%.
c. 4%.
d. None of the above.
138
Exercises
Suppose that the 1-year interest rate in the US is 5%, the spot exchange rate is $0.75 = €1 and
the 1-year forward rate is $0.75 = €1. What must the one-year interest rate in France if the IRP
between France and the US holds?
a. 5%.
b. 6%.
c. 4%.
d. None of the above.
139
Exercises
Suppose that the 1-year interest rate in the US is 8%, the spot exchange rate is $1 = €1 and the
1-year interest rate in France is 8%. What must the one-year forward exchange rate be (if the
IRP between France and the US holds)?
a. $0.75 = €1.
b. $0.50 = €1.
c. $0.80 = €1.
d. None of the above.
140
Exercises
Suppose that the 1-year interest rate in the US is 8%, the spot exchange rate is $1 = €1 and the
1-year interest rate in France is 8%. What must the one-year forward exchange rate be (if the
IRP between France and the US holds)?
a. $0.75 = €1.
b. $0.50 = €1.
c. $0.80 = €1.
d. None of the above.
141
Violation of IRP and Arbitrage
• Consider now the following set of foreign and domestic interest rates and spot
and forward exchange rates. Is there a violation of IRP?
Spot exchange rate
S($/£) = $1.5/£
360-day forward rate
F360($/£) = $1.480/£
US interest rate
i$ = 5.0%
British interest rate
i£ = 8.0%
Violation of IRP and Arbitrage
• Consider now the following set of foreign and domestic interest rates and spot
and forward exchange rates. Is there a violation of IRP?
Spot exchange rate
S($/£) = $1.5/£
360-day forward rate
F360($/£) = $1.480/£
US interest rate
i$ = 5.0%
British interest rate
i£ = 8.0%
• Arbitrage opportunity exists because IRP does not hold
𝐹
1.48
(1 + 𝑖£ ) =
(1.08) = 1.0656 > (1 + 𝑖$ ) = 1.05
𝑆
1.50
• Arbitrage starts with borrowing either $1,000,000 or £666,667
- Rule of thumb is to borrow from country with lower interest rate
Violation of IRP and Arbitrage
• A trader can borrow $1,000,000
- repayment in one year will be $1,050,000 [=$1,000,000(1+ i$)=$1,000(1.05)]
- always borrow in country with lower interest rate (in this case US at 5%)
• Buy £666,667 spot using $1,000,000
• Invest £666,667 in UK and receive at maturity £666,667 1.08=£720,000
• Sell £720,000 forward in exchange for $1,065,600 [=£720,000 ($1.48/£)]
• After one year trader receives $1,065,600
• Once she repays the loan of $1,000,000 (principal) plus interests, she will still
have $15,600 (=$1,065,600 - $1,050,000) which is a riskless profit
• How long arbitrage opportunity last? Only a short while!
IRP as an equilibrium condition
• To make riskless profits a trader (arbitrageur actually) will
- borrow US $ as much as possible (this implies that i$ ↑)
- buy £ for US$ spot (implying £ will appreciate, i.e. S($/£)↑)
- lend in UK as much as possible (this implies that i£ ↓)
- sell pounds for US $ forward (implying £ will depreciate in forward market, i.e. F($/£) ↓
• Movements in i$ , i£ , S($/£) and F($/£) will raise 1 + 𝑖$ and lower (F/S)(1 + i£)
of IRP relationship until both side are equalized (and IRP restored)
F
(1 + i£ ) ,
S
(1 + i$ ) 
Violation of IRP and Arbitrage (2)
• Consider now the following set of foreign and domestic interest rates and spot
and forward exchange rates. Does IRP hold ?
Spot exchange rate
S(€/$) = €0.8/$
90-day forward rate
F90(€/$) = €0.7994/$
U.S. interest rate
i$ = 8.0%
Germany interest rate
iger = 5.0%
Violation of IRP and Arbitrage (2)
• Consider now the following set of foreign and domestic interest rates and spot
and forward exchange rates. Does IRP hold ?
Spot exchange rate
S(€/$) = €0.8/$
90-day forward rate
F90(€/$) = €0.7994/$
U.S. interest rate
i$ = 8.0%
Germany interest rate
iger = 5.0%
• Note: both forward rate and interest rates should have same maturity.
• Notice that here time horizon is 90 days and indirect rates S and F
- Quarterly or three-month interest rates are 8.0/4=2.0 and 5.0/4=1.25
- direct rates are S($/€)=1/0.8=$1.25/€ and F90($/€)=1/0.7994=$1.2510/€
Violation of IRP and Arbitrage (2)
• Consider now the following set of foreign and domestic interest rates and spot
and forward exchange rates. Does IRP hold ?
Spot exchange rate
S(€/$) = €0.8/$
90-day forward rate
F90(€/$) = €0.7994/$
U.S. interest rate
i$ = 8.0%
Germany interest rate
iger = 5.0%
• Arbitrage opportunity exists because IRP does not hold
𝐹($/€)
1.2510
1 + 𝑖𝐺𝑒𝑟 =
1.0125 = 1.0133 < 1 + 𝑖$ = 1.02
𝑆($/€)
1.25
• Assume arbitrageur can borrow $1,000,000 or €800,000
Violation of IRP and Arbitrage (2)
• Borrow in Germany €800,000 where interest rate is lower (5% vs 8%)
- repayment in three months is €810,000 [=€800,000(1+ i€)=€800,000(1.0125)]
• Buy $1,000,000 spot using €800,000
• Invest $1,000,000 in US and receive in three months $1,000,0001.2=
$1,020,000
• Buy forward €815,347.722 [=$1,020,000/1.2510]
• Once loan is repaid trader will still have €5,347.722 (=€815,347.722 - €810,000)
which is a riskless profit
• Or in USD it will be $6,690
Reasons for Deviations from IRP
• IRP tends to hold quite well, in general (for long run)!
• IRP might not hold precisely because of transaction costs and capital controls
• Transactions Costs
- there may be fees for the purchasing of FX spot and forward as well as fees on loans
which prevent IRP to hold precisely
• Capital Controls
- governments sometimes restrict import/export of money through taxes or outright bans
so that arbitrage opportunities cannot be exploited
Exercises
Suppose you observe the following exchange rates: S($/€) = 0.85 (i.e. €1 = $.85) The
one-year forward rate is F1($/€) = 0.935 (i.e. €1 = $.935) The risk-free interest rate in
the U.S. is 5% and in Germany it is 2%. How can a dollar-based investor make money?
a. Borrow dollars in the U.S., exchange for euros, invest in Germany, enter into a onyear forward contract; in one year, translate the euros back into dollars at the forward
rate.
b. Borrow euros, translate into dollars at the spot, invest in the U.S. at 5% for one year.
At the end of the year, translate part of your dollar investment back into euros at the
forward rate to repay your euro debt.
c. There are no profitable arbitrage opportunities.
151
Exercises
Suppose you observe the following exchange rates: S($/€) = 0.85 (i.e. €1 = $.85) The
one-year forward rate is F1($/€) = 0.935 (i.e. €1 = $.935) The risk-free interest rate in
the U.S. is 5% and in Germany it is 2%. How can a dollar-based investor make money?
a. Borrow dollars in the U.S., exchange for euros, invest in Germany, enter into a onyear forward contract; in one year, translate the euros back into dollars at the forward
rate.
b. Borrow euros, translate into dollars at the spot, invest in the U.S. at 5% for one year.
At the end of the year, translate part of your dollar investment back into euros at the
forward rate to repay your euro debt.
c. There are no profitable arbitrage opportunities.
𝐴𝑛𝑠𝑤𝑒𝑟 𝐴: 1$ 1 + 0.05 = 1.05$ (Borrow US $ at 5% interest rate)
1
× (1 + 0.02) × 0.935=1.122 (exchange US$ in Euros, invest in Ger, convert proceeds in US $)
0.85
𝐴𝑛𝑠𝑤𝑒𝑟 𝐵: 1€ 1 + 0.02 = 1.02 (Borrow € at 2% interest rate)
1
0.85 × (1 + 0.05) × 0.935=0.954 (exchange Euros in US$, invest in US, convert proceeds in Euros)
IRP and exchange rate determination
• IRP condition can be written as follows
1 + i£ 
S=
F
1 + i$ 
• Spot exchange rate St determined by
- forward rate Ft
- interest rate differential between US and UK
• Higher i$ implies lower S($/£), i.e. appreciation of $
- i$ ↑, capitals inflow to US, increased demand of $, appreciation of $ against £, S($/£)↓
• Higher i£ implies higher S($/£), i.e. depreciation of $
- i£ ↑, capitals flow into UK, increased demand of £, depreciation of $ against £, S($/£)↑
IRP and exchange rate determination
• Under certain conditions forward rates encompass correct expectations of future
spot rates conditional on all information available at time t
1 + i£ 
F = Et  St +1 I t   S = 
 Et  St +1 I t 
1 + i$ 
• This formula posits that spot rate St driven by expectations formed at time t about
future spot rate St+1, ie Et[St+1│It]
- thus expectations Et[St+1│It] is key determinant of St
• Two implications:
- when people expect exchange rate to go up in the future (say at t+1) then it goes up now
- as traders receive new information (news) continuously, they will revise expectations
Et[St+1│It] continuously
- as arrivals of news is unpredictable (random) also dynamic of spot rates St becomes
unpredictable
IRP and exchange rate determination
• Under certain conditions forward rates encompass correct expectations of future
spot rates conditional on all information available at time t
1 + i£ 
F = Et  St +1 I t   S = 
 Et  St +1 I t 
1 + i$ 
When forward rate is replaced by the expected future spot exchange rate, we can get following:
E(e) ≈ i$ – i€
E(e) is the expected rate of change in exchange rate 𝐸 𝑆𝑡+1 − 𝑆𝑡 /𝑆𝑡
Interest rate differential between two countries pair is equal (approximately) to the expected rate
of change in exchange rate. This is also called uncovered interest rate parity.
Currency Carry Trade
• Buying high yield, funding with low yield, no hedging.
• Currency carry trade involved buying a currency that has a high rate of interest
(high yield) and funding the purchase by borrowing in a currency with low rates of
interest (low yield), without any hedging.
• Is carry trade profitable ? Depends…
– The carry trade is profitable as long as the interest rate differential is greater than the
appreciation of the funding currency against the investment currency.
– Example:
– 1-year borrowing rate in Dollars is 2.01%; the 1-year lending rate in pounds is 1%.
– The direct spot ask exchange rate is $1.25/£.
– What should be the spot bid rate prevailing in one year for the currency carry trade to turn
out profitable?
Currency Carry Trade
• A trader who borrows $1m @ 2.01% will owe $1,020,100 in one year.
• Trading $1m for pounds today at the spot rate generates £800,000.
• This £800,000 invested for one year @ 1% will yield £808,000 (Future value).
• The currency carry trade will be profitable if the spot bid rate prevailing in one
year is high enough that his £808,000 will sell for at-least $1,020,100 (that is,
enough to repay his debt).
$1,020,100 $1.2625
=
£808,000
£1.00
Note that: one-year forward rate prevailing at time zero is unimportant here, since our
trader isn’t hedged.
So, it should not be less then $1.2625 for each £.
If at one year, the spot rate is $1.25, our trader will lose = $10,100
𝑏
𝑆360
=
Absolute and Relative PPP
Absolute Purchasing Power Parity
• Law of one price (LOOP) posits that the price of a certain good (for instance a
Ferrari car) must be the same across countries once measured in a common
currency
• When LOOP is applied internationally to standard commodity basket we have PPP
• Let P$ price in US$ of standard commodity basket in US, P£ the pound price of
same basket in UK and S($/£) is spot exchange rate (how many US$ needed to
buy 1£)
• PPP postulates that price of commodity baskets must be the same in US and UK
P$ = S($/£)·P£
PPP and Exchange Rate Determination
• Assume you know both P$ and P£ then can compute the theoretical (PPP-based)
exchange rate
P$
S($/£) =
P£
• PPP asserts that exchange rate between two currencies should equal the
ratio of the countries’ price levels
❖However, PPP probably doesn’t hold precisely in the real world
❖PPP-determined exchange rates still provide a valuable benchmark
•
For example, if a given basket of goods costs $300 in the US and £150 in the
UK then the price of that basket in terms of dollars should be:
P$
$300
S($/£) =
=
P£
£150
= $2/£
Exercises
The PPP posits that
a. The cost of a haircut in the US should be exactly the same as the cost in Hong Kong
b. Rates of inflation must be the same everywhere
c. Spot exchange rates are the best predictor of expected inflation rates
d. None of the above
Exercises
The PPP posits that
a. The cost of a haircut in the US should be exactly the same as the cost in Hong Kong
b. Rates of inflation must be the same everywhere
c. Spot exchange rates are the best predictor of expected inflation rates.
d. None of the above
Relative PPP
• When we consider rate of changes of P$, P£ and S($/£) we have the relative
version of PPP
- where e is rate of change of spot exchange rate S($/£), while $ and £ are inflation
rates in US and UK
 $ −  £ 
e=
  $ − £
 1+ £ 
• Relative PPP states that rate of change in exchange rate must be equal to
the differences in inflation rates
• If US inflation is 5% and UK inflation is 8% then the pound should ?????????
by ??? (more precisely by ???)
Relative PPP
• When we consider rate of changes of P$, P£ and S($/£) we have the relative
version of PPP
- where e is rate of change of spot exchange rate S($/£), while $ and £ are inflation
rates in US and UK
 $ −  £ 
e=
  $ − £
 1+ £ 
• Relative PPP states that rate of change in exchange rate must be equal to
the differences in inflation rates
• If US inflation is 5% and UK inflation is 8% then the pound should depreciate
by 3% (more precisely by 2.78%)
Relative PPP
• Suppose the spot exchange rate is $1.25 = €1.00.
• If the inflation rate in the U.S. is expected to be 3% in the next year and 5% in
the euro zone, then the rate of change in exchange rate is equal to the
differences in the rates of inflation – roughly 2%.
𝜋$ − 𝜋𝑒𝑢𝑟𝑜
𝑒=
1 + 𝜋𝑒𝑢𝑟𝑜
≅ 𝜋$ − 𝜋𝑒𝑢𝑟𝑜
• The euro will trade at a 1.90% discount in the forward market.
Expected Rate of Change in Exchange Rate as
Interest Rate Differential
E(e) =
F($/€) – S($/€)
S($/€)
i$ – i€
≈ i$ – i€
=
1 + i€
• Given the difficulty in measuring expected inflation, managers often use a
“quick and dirty” shortcut:
$ – € ≈ i$ – i€
• PPP attributed to Cassell’s writings in 1920s, but origins date back to David
Ricardo
Gustav Cassell
1866-1945
David Ricardo
1772-1823
167
Exercises
Assume that Absolute PPP initially holds. Derive the condition for the Relative PPP to hold.
Exercises
Assume that Absolute PPP initially holds. Derive the condition for the Relative PPP.
If Absolute PPP holds at initial period (say t=0) then S($/£) =
P$
P£
Price changes from period t=0 to t=1 due to inflation rates $ and £ so that in t=1 levels of
prices is P$ (1+ $) and P£(1+£)
Nominal rate S($/£) changes from period t=0 to t=1 is e($/£) so that in t=1 we can write that
S(1+e)
At t=1 level of UK prices expressed in US $ is P£(1+£)S(1+e)
At t=1 level of US prices (expressed in US $) is P$(1+$)
169
Exercises
According to Absolute PPP the % change in nominal rate (𝑒) should adjust to maintain the
parity between the new levels of prices in the US and UK so that
P£(1+£)S(1+e) = P$(1+$)
P$(1+$)
s(1 + 𝑒) =
P£(1+£)
Recalling that s =
P$
can write that P$ (1 + 𝑒) = P$(1+$)
P£
P£
P£(1+£)
(1 + 𝑒) =
(1+$)
(1+£)
(1+ )
e= (1+$ ) − 1
£
e($/£)=
1+$−1−£ $−£
(1+£) = 1+£
Exercises
Assume that the expected inflation for the next year is 20% for Turkey and 2% for the Euro
area. According to the Relative PPP the exchange rate Turkish Lira/Euro is expected to
a. Appreciate (ie less Turkish Lira will be needed to buy one Euro)
b. Appreciate by 18% (ie 18% less Turkish Lira will be needed to buy one Euro)
c. Depreciate by 18% (ie 18% additional Turkish Lira will be needed to buy one Euro)
d. None of the above
Exercises
Assume that the expected inflation for the next year is 20% for Turkey and 2% for the Euro
area. According to the Relative PPP the exchange rate Turkish Lira/Euro is expected to
a. Appreciate (ie less Turkish Lira will be needed to buy one Euro)
b. Appreciate by 18% (ie 18% less Turkish Lira will be needed to buy one Euro)
c. Depreciate by 18% (ie 18% additional Turkish Lira will be needed to buy one Euro)
d. None of the above
e(£/€)= Π£ − Π€ =20 – 2 = 18
Exercises
As of 25th of March 2019, the exchange rate between the Brazilian real and US $ is R$1.95/$.
The consensus forecast for the US and Brazil inflation rates for the next 1-year period is 2.6%
and 20%, respectively. How would you forecast the exchange rate to be at around the 25th of
March 2020?
Exercises
As of 25th of March 2019, the exchange rate between the Brazilian real and US $ is R$1.95/$.
The consensus forecast for the US and Brazil inflation rates for the next 1-year period is 2.6%
and 20%, respectively. How would you forecast the exchange rate to be at around the 25th of
March 2020?
Using Relative PPP to forecast the exchange rate S(R$/$)
E(e)= E(R$) - E($)= 20 - 2.6 = 17.4%.
Thus the Brazilian real is expected to depreciate by 17.4% (ie exchange rate R$/$ is going up).
The exchange rate level in one year is E(ST) = So(1 + E(e))= (R$1.95/$)×(1 + 0.174)= R$2.29/$.
174
Exercises (alternative solution)
As of 25th of March 2019, the exchange rate between the US$ and Brazilian real $0.5128/R$.
The consensus forecast for the US and Brazil inflation rates for the next 1-year period is 2.6%
and 20%, respectively. How would you forecast the exchange rate to be at around the 25th of
March 2020?
Using Relative PPP to forecast the exchange rate S($/R$)
E(e)= E($) - E(R$)= 2.6 - 20 = -17.4%
Thus the US $ is expected to appreciate by 17.4% (ie exchange rate $/R$ is going down).
The exchange rate level in one year is E(ST) = So(1 + E(e))= ($0.5128/R$)×(1 - 0.174)=
=($0.5128/R$)×0.826 = $0.4235/R$.
175
Empirical Tests of PPP Theory
(Does the PPP hold?)
Actual JPY/USD and (calculated) PPP Exchange Rates
Actual USD/GBP and (calculated) PPP Exchange Rates
Actual USD/Euro and (calculated) PPP Exchange Rates
% changes in $/£ rate and inflation differential (US-UK)
Evidence on PPP
•
General evidence is that Absolute and Relative PPP do not hold at least in the
short-run (ie over short time horizons of 3-5 years) so that
- price ratio and level of exchange rates not aligned (Absolute PPP)
- inflation differentials and changes in level of exchange rates not aligned (Relative PPP)
•
•
PPP holds up well over the very long-run but is poor for short-run horizons
PPP holds better for countries with relatively high rates of inflation and
underdeveloped capital markets
- e.g. evidence in favour of PPP for Turkish lira – US$ exchange rate
- strong departures from PPP for Euro-US$ exchange rate
Evidence on PPP
• The PPP may not hold because
- Exchange rates also affected by differentials in interest rates, income levels, political risk, etc.
- Baskets of commodities not identical across countries
- Many services are not tradable (eg hair cuts, driving school tuitions, etc) and therefore not
exposed to arbitrage forces (remember here the LOOP)
- Trade barriers (tariff etc.) and transportation costs
• However, PPP-based exchange rates still provide valuable benchmark to
determine whether an exchange rate is overvalued or undervalued
Exercise
Consider diagram below which depicts % changes in S($/£) rate (dotted line) and the inflation
differential between the US and UK (solid line).
a. Relative PPP holds because volatility of S($/£) and inflation differential is similar
b. Relative PPP holds because volatility of S($/£) is greater than that of inflation differential
c. Relative PPP doesn’t hold as volatility of S($/£) is greater than that of inflation differential
d. None of the above
Exercise
Consider diagram below which depicts % changes in S($/£) rate (dotted line) and the inflation
differential between the US and UK (solid line).
a. Relative PPP holds because volatility of S($/£) and inflation differential is similar
b. Relative PPP holds because volatility of S($/£) is greater than that of inflation differential
c. Relative PPP doesn’t hold as volatility of S($/£) is greater than that of inflation differential
d. None of the above
The Fisher Effect (FE)
• An increase (decrease) in the expected rate of inflation will cause a proportionate
increase (decrease) in the nominal interest rate
Irvin Fisher
1867-1947
The Fisher Effect (FE)
• For the US the Fisher relationship written as
1 + i$ = (1+ $)E(1+$) = 1 + $ + E[$] + $E[$]
i$ = $ + E[$] + $E[$] $ + E[$]

where
$ is equilibrium expected “real” US interest rate,
E[$] is expected rate of US inflation and
i$ is equilibrium expected nominal US interest rate
$E[$] negligible term (product of two small figures) that you can drop from above formula
FE and expected inflation
• The Fisher relationship maintains that expected inflation rate E[$] is
approximated as the difference between the nominal and real interest rates in
each country
i$ = $ + (1+ $)E[$]
i$ -$ = (1+ $)E[$]
E[$] =(i$-$)/(1+ $)  i$ -$
Exercise
Due to the integrated nature of their capital markets, investor in both the US and Great Britain
require the same expected real interest rate of 3 percent. The expected annual inflation in the US
is 2 percent and in the UK expected annual inflation is 5%. The spot exchange rate is currently
£1.00 = $1.80. Calculate the nominal interest rates in the UK and US assuming the Fisher effect
holds.
a. 3% in both countries
b. 8.15% in the UK and 5.06% in US
c. 1% in the US and 2% in the UK
d. 8% in the US and 5% in the UK
Exercise
Due to the integrated nature of their capital markets, investor in both the US and Great Britain
require the same expected real interest rate of 3 percent. The expected annual inflation in the US
is 2 percent and in the UK expected annual inflation is 5%. The spot exchange rate is currently
£1.00 = $1.80. Calculate the nominal interest rates in the UK and US assuming the Fisher effect
holds.
a. 3% in both countries
b. 8.15% in the UK and 5.06% in US [i$ =0.03+0.02+0.03∙0.02=0.0506]
c. 1% in the US and 2% in the UK
d. 8% in the US and 5% in the UK
International Fisher Effect (IFE)
• Assume Fisher effect holds in US and UK
E[$] =(i$-$)/(1+ $)  i$ -$
E[£] =(i£-£)/(1+ £)  i£ -£
• Assume also that real rates are the same in both countries
$ = £
• Assume relative PPP holds so that 𝐸 𝑒 = 𝐸 𝜋$ − 𝐸(𝜋ℒ )
• Then substituting above relationships into relative PPP we get IFE:
𝐸 𝑒 = 𝐸 𝜋$ − 𝐸 𝜋ℒ ≅ 𝑖$ − 𝑖ℒ
• IFE suggests that nominal interest rate differential reflects expected changes
in exchange rate
Forward Expectations Parity (FEP)
• FEP can be constructed observing that IRP can written as follows
𝐹 1 + 𝑖$
𝐹
1 + 𝑖$
𝐹 − 𝑆 1 + 𝑖$ − 1 − 𝑖ℒ 𝑖$ − 𝑖ℒ
=
⇒ −1=
−1 ⇒
=
=
≅ 𝑖$ − 𝑖ℒ
𝑆 1 + 𝑖ℒ
𝑆
1 + 𝑖ℒ
𝑆
1 + 𝑖ℒ
1 + 𝑖ℒ
• As long as IRP and IFE (𝐸 𝑒 = 𝑖$ − 𝑖ℒ ) hold then we can write
𝐹−𝑆
≅ 𝐸(𝑒)
𝑆
which is the FEP
• FEP asserts that any forward premium (discount) is equal to the expected change in exchange
rate
Equilibrium Exchange Rate Relationships
E(e)
F–S
(i$ – i£)
S
E($ – £)
Equilibrium Exchange Rate Relationships
𝐹−𝑆
≅ 𝑖$ − 𝑖ℒ
𝑆
(i$ – i£)
E(e)
F–S
IRP
S
E($ – £)
Equilibrium Exchange Rate Relationships
E(e)
PPP
(i$ – i£)
IRP
𝐸 𝑒 = 𝐸 𝜋$ − 𝐸(𝜋ℒ )
F–S
S
E($ – £)
Equilibrium Exchange Rate Relationships
𝐸 𝑒 ≅ 𝑖$ − 𝑖ℒ
E(e)
IFE
PPP
(i$ – i£)
IRP
F–S
S
E($ – £)
Equilibrium Exchange Rate Relationships
𝐹−𝑆
≅ 𝐸(𝑒)
𝑆
E(e)
IFE
FEP
PPP
(i$ – i£)
IRP
F–S
S
E($ – £)
Futures on Foreign Exchange
Learning Objectives:
- Similarities between forward and futures contracts
- Currency futures markets
- Basic currency futures relationships
Material can be found in Eun and Resnick, chapter 7
Let’s Recap on Forward contracts…
• Forward contract has two “legs”: on the maturity date of the contract, the bank promises to pay a
known amount of one currency, and the customer promises to pay a known amount of another
currency.
• However, from the bank’s point of view, the credit risk present in forward contract is of a different
nature to the credit risk present in a loan.
For e.g: on Default risk of Forward contract:
• Company C bought forward USD 1m against EUR.
• The bank, which has to deliver USD 1m, bought that amount in the interbank market to hedge its
position.
• If company C defaults, the bank has the right to withhold the delivery of USD 1m.
• However, the bank still has to take delivery of (and pay for) the USD it had agreed to buy in the
interbank market at a price 𝐹𝑡0,𝑇 .
• Having received the (now unwanted) USD, the bank has no choice but to sell these USD in the spot
market.
• Given default by company C, the bank therefore has a risky cash flow of 𝑆𝑇 − 𝐹𝑡0,𝑇
Let’s Recap on Forward contracts…
• The second problem with forward contract is the lack of secondary markets.
• Each forward contract is tailor made in terms of its maturity and contract amount, and not
many people are likely to be specifically interested in your contract.
• Also, for this contract you probably had to provide extra security to cover default risk.
• This means that your bank may not want you to be replaced by somebody else as a
counterparty, unless comparable security is arranged (an unwanted hassle for bank!) or you
yourself guarantee the payment (very dangerous!).
• So, in forward contract, the problem of illiquidity is partly explained by the credit risk
problem.
• Lets look at the example in next slide!
Let’s Recap on Forward contracts…
• Suppose a Spanish wine merchant receives an order for ten casks of 1930 Amontillado,
worth USD 1,234,567.89 and payable in 90 days, from a (then) rich American, Mr. Fon
Bump.
• The Spanish merchant is happy about the order. And he hedges this transaction by selling the
USD forward.
• However, after 35 days, Mr. Fon Bump scandal gets the limelight and goes bankrupt (again).
This means he is obviously unable to pay for the wine to Spanish merchant.
• The Spanish merchant (exporter) would like to get out the forward contract, but it is not easy
to find someone else who also want to sell forward exactly USD 1,234,567.89 for 55 days
(90-35=55days) from the current date.
• Also, another problem is : the wine merchant would have to convince his banker that the
new counterparty is at-least as credit worthy as himself.
Let’s Recap on Forward contracts…
What are the ways of reducing Default Risk in the Forward Market?
• There are some smart solutions that banks use that partially solve the problem
of default risks:
• Right of offset; credit lines; credit agreements and security; restricted applications and
shorter lives with an option to roll over if all goes well !
• But, the second problem of illiquidity that is due to the absence of secondary
market is not addressed in above solutions.
• The idea is that: a long and short should add up to a zero position if there a default. But, in
forward contract, it does not add up to zero position in case of default.
How Future contracts Differ from Forward Contract ?
In general, a currency future contract has the following key characteristics:
1) It has zero initial value
▪ symmetry between buyer and seller;
▪ at the start of contract there is no intrinsic value;
▪ at the time of inception there are no unrealized gains or losses, making the value of contract effectively
zero for both parties.
2) It stipulates delivery of a known number of forex units on a known future date 𝑇
3) The Home Currency payment for the forex is a known amount 𝑓𝑡,𝑇 , paid later
The only news here, relative to forward contract, is the last word – the vague term “later” rather than the precise
expression “at 𝑇”
Forward contracts are not really traded, they are simply initiated in the over-the-counter (OTC) typically with the
client’s bank and held until maturity.
Future contracts can be transferred among investors (standardized contracts, in organized markets, and with
clearing corporation as the central counterpart).
Futures Contracts: Preliminaries
• A futures contract is similar to a forward contract as
- It specifies that a certain currency will be exchanged for another at a specified time in the
future at prices specified today
• However futures contracts are also different from forward contracts
• Forward contracts are
- tailor-made (in terms of size/expiration date) to needs of customers (over-the-counter)
- traded by bank dealers via electronic networks
- no daily resettlement (ie participants honor contracts by buying/selling pre-agreed
amount of foreign currency at maturity at agreed forward price)
• Futures contracts are instead
- standardized contracts
- trading on organized (centralized) exchanges
- with daily resettlement through a clearinghouse
Futures Contracts: Preliminaries
• Standard features are
- Contract Size: amount of underlying foreign currency for future purchase or sale
- Delivery Month: Mar, Jun, Sept and Dec
- Daily resettlement: positions (long or short) are “regulated” on daily basis (unlike in
forward contracts where positions are “regulated” only once at expiration date)
• Futures feature also so-called “Initial performance bond” which is the amount
that must be deposited in a collateral account
- equivalent to about 2-5% of contract value
- in cash or T-bills held and kept at brokerage house
- it is ‘good faith money’ that holder of contract will honor his/her obligations
- account balances fluctuate up/down as a result of daily resettlements
Exercise
Futures contracts are typically _______; forward contracts are typically _______.
a. sold on an exchange; sold on an exchange
b. offered by commercial banks; sold on an exchange
c. sold on an centralized exchange; offered by commercial banks
d. offered by commercial banks; offered by commercial banks
Exercise
Futures contracts are typically _______; forward contracts are typically _______.
a. sold on an exchange; sold on an exchange
b. offered by commercial banks; sold on an exchange
c. sold on an centralized exchange; offered by commercial banks
d. offered by commercial banks; offered by commercial banks
Daily Resettlement
• With Forward contracts, it states a price for the future transaction.
• But, with futures contracts, we have daily resettlement of gains and losses rather than one
big settlement at maturity i.e., marked-to-market
• Every trading day with future contracts:
• If the price goes down, the long pays the short
• Short position benefits since they agreed to sell at higher price
• If the price goes up, the short pays the long
• Long position benefits since they agreed to buy at a lower price
• Short position loses because they agreed to sell at a lower price than the new higher price prevailing in
the market.
• Thus, after the daily resettlement, each party has a new contract at the new price with oneday-shorter maturity
• The change in settlement prices from one day to the next determines the settlement amount.
Daily Resettlement: An Example
• Consider a long position in the CME (Chicago Mercantile Exchange) Euro/US
Dollar contract
• It is written on €125,000 and quoted in $ per €
• The strike price is $1.30 and maturity is 3 months
- so long position agrees to buy €125,000 in 3 months at rate $1.30=1€
• At initiation of contract, the long position posts at 4% an “initial performance
bond” of $6,500 in his collateral account
• The maintenance performance bond is $4,000
- meaning that whenever balance becomes < $4,000 then minimum level of $4,000
must be restored
Daily Resettlement: An Example
• Recall that an investor with a long position gains from increases in the price of
the underlying asset (€ currency)
• Our investor has agreed to buy €125,000 at $1.30 per euro in three months time
• With a forward contract, if at expiration date the € was worth $1.24 then he
would lose as much as (counterparty in short position will receive from him)
$7,500 = ($1.24 – $1.30) × 125,000.
• If instead at expiration date € was worth $1.35, he would gain (counterparty in
short position will pay him)
$6,250 = ($1.35 – $1.30) × 125,000
• In forward contracts above gains/losses are settled only once at expiration date,
so there is no daily resettlement
Daily Resettlement: An Example
• In futures contracts there are daily resettlement of gains/losses rather than one
big settlement at maturity (like for forward contracts)
• Every trading day
- if the price (spot exchange rate) goes down, the long party pays the short counter-party
- if the price (spot exchange rate) goes up, the short party pays the long counter-party
• After the daily resettlement, each party enters a new future contract at the new
price (most recent spot rate) with one-day shorter maturity
Performance Bond Money
• Each day’s losses are subtracted from the investor’s collateral account
• Each day’s gains are added to the investor’s account
• In this example, at initiation the long position posts an initial performance bond
of $6,500
• Assume that the “maintenance” level is $4,000
- If this investor loses more than $2,500 (=6,500 – 4,000) then to maintain his long
position he has to top up his account
- If investors cannot deposit additional funds will have his position liquidated
Daily Resettlement: An Example
• Assume over the first 3 days, the euro strengthens then depreciates in dollar
terms:
Settle
Gain/Loss
Account Balance
$1.31
$1,250 =$0.01×125,000 $7,750
= $6,500 + $1,250
$1.30
–$1,250 =-$0.01×125,000 $6,500
= $7,750 - $1,250
$1.27
–$3,750 =-$0.03×125,000 $2,750
= $6,500 - $3,750
• On third day suppose our investor keeps his long position open by posting
an additional $3,750 in his account
Daily Resettlement: An Example
• Over the next 2 days, the long position keeps losing money as rate $/€
decreasing (ie $ appreciates against €)
Settle
Gain/Loss
Account Balance
$1.31
$1,250
$7,750
= $6,500 + $1,250
$1.30
–$1,250
$6,500
= $7,750 - $1,250
$1.27
–$3,750
$6,500
= $6,500 - $3,750 + $3,750
$1.26
–$1,250
$5,250
= $6,500 – $1,250
$1.24
–$2,500
$2,750
= $5,250 – $2,500
Toting Up
• At the end of the fifth day of contract our investor has three ways of
computing his gains and losses:
• Sum of daily gains and losses
– $7,500 = $1,250 – $1,250 – $3,750 – $1,250 – $2,500
• Contract size times the difference between initial contract price ($1.30/€) and last
settlement price ($1.24/€ ).
– $7,500 = ($1.24/€ – $1.30/€) × €125,000
• Ending balance on account ($2,750) minus beginning balance on account ($6,500),
adjusted for additional deposits ($3,750) or withdrawals
– $7,500 = $2,750 – ($6,500 + $3,750)
Daily Resettlement: An Example
Settle
Gain/Loss
Account Balance
$1.30
–$–
$6,500
$1.31
$1,250
$7,750
$1.30
–$1,250
$6,500
$1.27
–$3,750
$2,750 + $3,750
$1.26
–$1,250
$5,250
$1.24
–$2,500
$2,750
= ($1.24 – $1.30) × 125,000
Total loss = – $7,500
= $2,750 – ($6,500 + $3,750)
Daily Resettlement: An Example
Holder of (long) futures
€125,000 at $1.30/1 €
in 3 months
Holder of (short) futures
€125,000 at $1.30/1 €
in 3 months
Daily Resettlement: An Example
Clearing House
(has always a buyer (long) and a
seller (short) for each contract)
Holder of (long) futures
€125,000 at $1.30/1 €
in 3 months
Holder of (short) futures
€125,000 at $1.30/1 €
in 3 months
Both the long and short positions
hold an account at the clearing house
Daily Resettlement: An Example
Clearing House
(has always a buyer (long) and a
seller (short) for each contract)
Both the long and short positions
hold an account at the clearing house
When the long position makes a daily
payment to clearing house
Holder of (long) futures
€125,000 at $1.30/1 €
in 3 months
Holder of (short) futures
€125,000 at $1.30/1 €
in 3 months
The clearing house transfers such
payment onto the account of the short
position
Daily Resettlement: An Example
Clearing House
(has always a buyer (long) and a
seller (short) for each contract)
Both the long and short positions
hold an account at the clearing house
When the short position makes a daily
payment to clearing house
Holder of (long) futures
€125,000 at $1.30/1 €
in 3 months
Holder of (short) futures
€125,000 at $1.30/1 €
in 3 months
The clearing house transfers such
payment onto the account of the long
position
Exercise
Assume today’s settlement price on a CME EUR futures contract is $1.3140/EUR. Assume that
EUR 125,000 is the contractual size of one EUR contract. You have a short position in one
contract. Your performance bond account currently has a balance of $1,700. The next three
days’ settlement prices are $1.3126, $1.3133, and $1.3049. Calculate the changes in the
performance bond account from daily marking-to-market and the balance of the performance
bond account after the third day.
Exercise
Assume today’s settlement price on a CME EUR futures contract is $1.3140/EUR. Assume that
EUR 125,000 is the contractual size of one EUR contract. You have a short position in one
contract. Your performance bond account currently has a balance of $1,700. The next three
days’ settlement prices are $1.3126, $1.3133, and $1.3049. Calculate the changes in the
performance bond account from daily marking-to-market and the balance of the performance
bond account after the third day.
Solution:
$1,700 + [($1.3140 - $1.3126) + ($1.3126 - $1.3133) + ($1.3133 - $1.3049)] x EUR125,000 =
=1,700+175-87.5+1,050=$2,837.5
where EUR 125,000 is the contractual size of one EUR contract.
222
Exercise
Do problem above again assuming you have a long position in the futures contract.
Exercise
Do problem above again assuming you have a long position in the futures contract.
Solution:
$1,700 + [($1.3126 - $1.3140) + ($1.3133 - $1.3126) + ($1.3049 - $1.3133)] x EUR125,000 =
=1,700-175+87.5-1,050 =$562.50.
Notice that, with only $562.50 in your performance bond account, you would need to top up
with additional funds your account to bring the balance back up to the initial performance bond
level.
Exercise
Compare and contrast the cash flows of short and long position in the futures contract.
Solution:
Long: [($1.3126 - $1.3140) + ($1.3133 - $1.3126) + ($1.3049 - $1.3133)] x EUR125,000 =
-175+87.5-1,050
Short: [($1.3140 - $1.3126) + ($1.3126 - $1.3133) + ($1.3133 - $1.3049)] x EUR125,000 =
175-87.5+1,050
Currency Futures Markets
• The Chicago Mercantile Exchange (CME) is by far the largest
• Others include:
• The Philadelphia Board of Trade (PBOT)
• The Tokyo International Financial Futures Exchange
• The London International Financial Futures Exchange
The Chicago Mercantile Exchange
• Expiry cycle: March, June, September, December
• Delivery date: third Wednesday of delivery month
• Last trading day: the second business day preceding the delivery day
• CME hours: 7:20 am to 2:00 pm CST
Reading Currency Futures Quotes
OPEN HIGH LOW SETTLE CHG
LIFETIME
OPEN
INT
HIGH LOW
Euro/US Dollar (CME)—€125,000; $ per €
Mar 1.3136 1.3167 1.3098 1.3112 -.0025 1.3687 1.1363 159,822
Jun 1.3170 1.3193 1.3126 1.3140 -.0025 1.3699 1.1750 10,096
Highest and lowest
prices over the life
Daily Change
of the contract.
Opening price
Lowest price that day
Number of open contracts
Highest price that day
Expiry month
Closing price
Open interest
• Open Interest refers to the number of contracts outstanding for a particular
delivery month
• Open interest is a good proxy of demand for a given contract
• Some refer to open interest as the depth of the market. The breadth of the
market would be how many different contracts (expiry month, currency)
are outstanding
Reading Currency Futures Quotes
OPEN HIGH LOW SETTLE CHG
LIFETIME
OPEN
INT
HIGH LOW
Euro/US Dollar (CME)—€125,000; $ per €
Mar 1.3136 1.3167 1.3098 1.3112 -.0025 1.3687 1.1363 159,822
Jun 1.3170 1.3193 1.3126 1.3140 -.0025 1.3699 1.1750 10,096
Sept 1.3202 1.3225 1.3175 1.3182 -.0025 1.3711 1.1750
600
• Notice that open interest is greatest in nearby contracts, in this case March.
In general, open interest typically decreases with term to maturity of
most futures contracts.
Basic Currency Futures Relationships
OPEN HIGH LOW SETTLE CHG
LIFETIME
OPEN
INT
HIGH LOW
Euro/US Dollar (CME)—€125,000; $ per €
Mar 1.3136 1.3167 1.3098 1.3112 -.0025 1.3687 1.1363 159,822
• Holder of a long position commits to pay $1.3112 per euro for €125,000—a
$163,900 (=125,000×1.3112) position.
• As there are 159,822 contracts outstanding, this represents a notational
principal of over $26 billion (=163,900×159,822)!
Basic Currency Futures Relationships
OPEN HIGH LOW SETTLE CHG
LIFETIME
OPEN
INT
HIGH LOW
Euro/US Dollar (CME)—€125,000; $ per €
Mar 1.3136 1.3167 1.3098 1.3112 -.0025 1.3687 1.1363 159,822
• Notice that if you had been smart (or lucky) enough to open a long position
at the lifetime low of $1.1363 by now your gains would have been
$21,862.50 = ($1.3112/€ – $1.1363/€) × €125,000
• Bear in mind that someone was unwise (unlucky) enough to take the short
position at $1.1363!
Reading Currency Futures Quotes
• Futures contracts can be seen as forward contracts, as such IRP can be
applied!
OPEN HIGH LOW SETTLE CHG
LIFETIME
OPEN
INT
HIGH LOW
Euro/US Dollar (CME)—€125,000; $ per €
Mar 1.3136 1.3167 1.3098 1.3112 -.0025 1.3687 1.1363 159,822
Jun 1.3170 1.3193 1.3126 1.3140 -.0025 1.3699 1.1750 10,096
Sept 1.3202 1.3225 1.3175 1.3182 -.0025 1.3711 1.1750
• Recall interest rate parity (IRP) condition is
1 + i$
F($/€)
=
1 + i€
S($/€)
600
Reading Currency Futures Quotes
OPEN HIGH LOW SETTLE CHG
LIFETIME
OPEN
INT
HIGH LOW
Euro/US Dollar (CME)—€125,000; $ per €
Mar 1.3136 1.3167 1.3098 1.3112 -.0025 1.3687 1.1363 159,822
Jun 1.3170 1.3193 1.3126 1.3140 -.0025 1.3699 1.1750 10,096
Sept 1.3202 1.3225 1.3175 1.3182 -.0025 1.3711 1.1750
600
From June to September we should expect higher interest rates i$ in $
denominated accounts (according to IRP)
- if we find instead a higher rate in € denominated account, we may have found
arbitrage opportunities!
Exercises
Assume that the June 2019 Mexican peso futures contract has a price of $0.08845. Assume that
MP500,000 is the contractual size of one MP contract. You believe the spot price in June will be
$0.09500. What speculative position would you enter into to attempt to profit from your
beliefs? Calculate your anticipated profits, assuming you take a position in three contracts. What
is the size of your profit (loss) if the futures price is indeed an unbiased predictor of the future
spot price and this price materializes?
Exercises
Assume that the June 2019 Mexican peso futures contract has a price of $0.08845. Assume
that MP500,000 is the contractual size of one MP contract. You believe the spot price in June
will be $0.09500. What speculative position would you enter into to attempt to profit from your
beliefs? Calculate your anticipated profits, assuming you take a position in three contracts. What
is the size of your profit (loss) if the futures price is indeed an unbiased predictor of the future
spot price and this price materializes?
If you expect the Mexican peso to rise from $0.08845 to $0.09500, you would take a long
position in futures since the futures price of $0.08845 is less than your expected spot price.
Your anticipated profit from a long position in three contracts is: 3 x ($0.09500 - $0.08845) x
MP500,000 = $9,825.00, where MP500,000 is the contractual size of one MP contract.
If the futures price is an unbiased predictor of the expected spot price, then the futures price is
$0.08845/MP. If this spot price materializes then will not make any profits or losses from your
position in three futures contracts: 3 x ($0.08845 - $0.08845) x MP500,000 = 0.
Exercises
Solve problem above assuming you believe the June 2019 spot price will be $0.07500.
Exercises
Solve problem above assuming you believe the June 2019 spot price will be $0.07500.
If you expect the Mexican peso to depreciate from $0.08845 to $0.07500, you would take a short
position in futures since the futures price of $0.08845 is greater than your expected spot price.
Your anticipated profit from a short position in three contracts is: 3 x ($0.08845 - $0.07500) x
MP500,000 = $20,175.00.
If the futures price is an unbiased predictor of the future spot price and therefore this price
materializes then you will not profit or lose from your short position.
Exercises
Assume that the Dec 2020 GBP futures contract has a strike price of $1.30 and that the
contractual size of one GBP contract is 125,000 GBP. At the end of Nov 2020 there will be the
last round of Brexit talks to strike a deal between the UK and EU. You believe that such a deal
will be eventually stroken, and that the GBP will benefit from that and will appreciate. For such
a reason you estimate that the spot price in Dec 2020 will be $1.50. What speculative position
would you enter into to attempt to profit from your beliefs? Calculate your anticipated profits,
assuming you take a position in the GBP contract.
Exercises
Assume that the Dec 2020 GBP futures contract has a strike price of $1.30 and that the
contractual size of one GBP contract is 125,000 GBP. At the end of Nov 2020 there will be the
last round of Brexit talks to strike a deal between the UK and EU. You believe that such a deal
will be eventually stroken, and that the GBP will benefit from that and will appreciate. For such
a reason you estimate that the spot price in Dec 2020 will be $1.50. What speculative position
would you enter into to attempt to profit from your beliefs? Calculate your anticipated profits,
assuming you take a position in the GBP contract.
If you expect the GBP to appreciate from $1.30 to $1.50 you should take a long position in
futures since the futures price of $1.30 is lower than your expected spot price.
Your anticipated profit from the long position is: ($1.50 - $1.30) x GBP125,000 = $25,000.
Exercises
• Graphical representation of pay-offs of long position
Long position
profit
If SDEC($/GBP) = 1.50 (therefore your prediction was right) long position must buy GBP
under the futures contract at the price $1.30 and can then sell in spot market at the price
$1.50, making a profit of ($1.50-$1.30) = $0.2 per GBP traded
0.2
0
FDEC($/GBP) =1.30 1.50
SDEC($/GBP)
loss
241
Exercises
Assume now that your expectations were wrong and that the spot price in Dec is $1.10.
Calculate profit/loss that the long position will deliver.
If the GBP depreciates from $1.30 to $1.10 and you are locked in a long position your loss
amount to : ($1.10 - $1.30) x GBP125,000 = -$25,000.
Exercises
• Graphical representation of pay-offs of long position
Long position
profit
1.10
0
FDEC($/GBP) =1.30
SDEC($/GBP)
-0.2
loss
If SDEC($/GBP) = 1.10 (therefore your prediction was wrong) long position must buy
GBP under the futures contract at the price $1.30 and can then sell in spot market at the
price $1.10, making a loss of ($1.10-$1.30) = -$0.2 per GBP traded
243
Options on Foreign Exchange Rates
Learning Objectives:
-
Definition on American and European options
Values of options at expiration date T
Values of American options at any time t prior to expiration date T (t<T)
Hedging FX risk using options
Options Contracts: Preliminaries
• An option gives the holder the right, but not the obligation, to buy or sell a
given quantity of an asset in the future, at prices agreed upon today
- similarities to forward/futures but no obligations to buy/sell
• Calls vs Puts
- Call option gives holder the right, but not the obligation, to buy a given quantity of a
specific asset at some point in time in future, at prices agreed upon today (the exercise
price)
- Put option gives holder the right, but not the obligation, to sell a given quantity of
asset at some point in time in future, at prices agreed upon today (the exercise price)
Note: buyer of an option are referred as the long; seller of an option is referred as the
writer
Options Contracts: Preliminaries
• European vs. American options
- European options can only be exercised on expiration date T
- American options can be exercised at any time t up to and including expiration
date T (i.e. at any time t≤T)
- If an American option is exercised prior to maturity, the person is said to have engaged in early
exercise.
- Since the possibility to exercise early generally has a value for the holder, American
options are usually worth more than European options, other things being equal
Options Contracts: Preliminaries
European-Style Call
• Suppose that you buy a call option on 1 NZD at GBP/NZD 0.50 expiring on June 30.
• You, as the buyer or owner of the right, are the holder of the option. You are “long the
call”.
• The counterparty, who grants you this right, is the seller or writer of the call. He has an
obligation to deliver 1 NZD to you at 50 cents if you want him to (that is, if you
exercise the option). So, he is “short the call”.
• The exercise price is GBP/NZD 0.50
• Thus, if the spot rate at time T turns out to be GBP/NZD 0.55 or 0.60, you will
exercise your right and buy NZD at GBP/NZD 0.50, and thus save NAD 0.05 or 0.10,
respectively.
• If spot rate at time T is less than 0.50, you will not exercise the option: there is no point
buying NZD from the writer at GBP/NZD 0.50 if you can obtain NZD for a lower
price in the spot market.
Options Contracts: Preliminaries
European-Style Call
• If your option is a call on NZD 12,500 at GBP/NZD 0.50, the writer may
have to deliver NZD 12,500 to you at 50 cents each.
• For a contract size of NZD 12,500, this means that if and when you decide
to exercise your call option, you will pay GBP 12,500 x 0.50 = GBP 6,250
for the NZD 12,500 , irrespective of the spot price at that moment.
• If the then-prevailing spot price is 0.60, you will have saved GBP 12,500 x
(0.60 – 0.50) = GBP 1,250
Options Contracts: Preliminaries
American-Style Call
• Suppose that you have an American call option to buy 1 unit of NZD at
GBP/NZD 0.50
• Currently, NZD trades at 0.48
• You will not exercise early: there is not point in paying GBP 0.50 if an
NZD can be bought spot for GBP 0.48.
• Suppose that, a few weeks later, the NZD has appreciated to 0.52.
• It might make sense to exercise early and earn 2 cents on the NZD.
• But, if the market price of the option at that moment is 3 cents, there is not
point in exercising early.
• Exercising nets the holder only 2 cents, while selling the option yields 3
cents.
Options Contracts: Preliminaries
• In-the-money: if the exercise of options generates a positive cash flows
- Call: exercise price (E) is less than spot price of underlying asset (ST)
- Put: exercise price (E) is greater than spot price of underlying asset (ST)
• At-the-money
- Call/Put: exercise price (E) is equal to spot price (ST) of the underlying asset
• Out-of-the-money
- Call: exercise price (E) is greater than spot price (ST) of underlying asset
- Put: exercise price (E) is less than spot price (ST) of underlying asset
Options Contracts: Preliminaries
• Intrinsic Value
- The difference between the exercise price of option (E) and the spot price of
underlying asset (St)
- You can also say: it is the option’s value if you had to make the exercise decision now.
- ITM: intrinsic value := Spot rate – Exercise rate (for call)
- ITM: intrinsic value := Exercise rate – Spot rate (for put)
- For OTM: the holder will not exercise immediately, so the intrinsic value is ZERO.
Option Premium
=
Intrinsic Value
+
Speculative Value
• Notice that option premium (i.e. market value of option) cannot be negative
- at most is zero
Options Contracts: Preliminaries
• Speculative Value
- The difference between option premium and intrinsic value of the option.
- Generally called Time Value of the option.
- Suppose, the NZD trades at 42.5, a put with strike price 43 has a positive
immediate exercise value of 0.5.
- However, there may be a consensus in the market that the (uncertain) prospects
of possible later exercise are worth even more than immediate exercise.
- The option would then trade above its intrinsic value of 0.5 cents, say at 0.55.
- The excess of the premiums over the intrinsic value is 0.05 : this is generally
called the time value of the option.
- Thus, we can always decompose an observed market price of an option into the
intrinsic value and residual time value:
𝑂𝑝𝑡𝑖𝑜𝑛 𝑣𝑎𝑙𝑢𝑒 = 𝑖𝑛𝑠𝑡𝑟𝑖𝑛𝑠𝑖𝑐 𝑣𝑎𝑙𝑢𝑒 + 𝑡𝑖𝑚𝑒 𝑣𝑎𝑙𝑢𝑒
Currency Options Markets
• Trading in Philadelphia Stock Exchange (PHLX)
• Trading is in six major currencies against US dollar
Currency
Australian dollar
British pound
Canadian dollar
Euro
Japanese yen
Swiss franc
Contract Size
AD50,000
£31,250
CD50,000
€62,500
¥6,250,000
SF62,500
Pay-off Profiles (holder of call option)
Profit
Long position in a call gives
holder option of buying set
quantity of currency at price E
Long 1
call
Option costs c0 (premium)
If the call is in-the-money, it is
worth ST – E.
If the call is out-of-the-money, –c0
it is worthless and the buyer of
the call loses his entire
investment of c0.
loss
45°
ST
E + c0
E
Out-of-money
In-the-money
Call: In-the-money: exercise price (E) is less than spot price of
underlying asset (ST)
Pay-off Profiles (seller of call option)
Profit
Writer of call is counterparty in
short position which must
fulfill obligation of selling a set
quantity of currency at price E
c0
to holder of call
ST
If the call is in-the-money, the
writer loses ST – E.
If the call is out-of-the-money,
the seller gains the option
loss
premium c0.
E + c0
E
Out-of-money
short 1
In-the-money
call
Bringing Call holder and seller together
Profit
Call (Holder)
45°
S*
-c0
E
loss
ST
Bringing Call holder and seller together
Profit
Call (Holder)
45°
c0
S*
-c0
ST
E
loss
45°
Call (Seller)
Pay-off Profiles (holder of put option)
Long position in put gives to
holder option of selling set Profit
quantity of currency at E
E – p0
If the put is in-the-money, it
is worth E – ST. The
maximum gain is E – p0
If the put is out-of-themoney, it is worthless and
the buyer of the put loses his – p0
entire investment of p0.
Put In-the-money: exercise price (E) is greater
than spot price of underlying asset (ST)
45°
ST
long 1
put
E – p0
E
loss
In-the-money
Out-of-money
Pay-off Profiles (seller of put option)
Writer of put is counterparty
in short position which must
Profit
fulfill obligation of buying a
set quantity of currency at
price E from holder
If the put is in-the-money, it
is worth E –ST. The
maximum loss is – E + p0
If the put is out-of-themoney, it is worthless and
the seller of the put keeps
the option premium of p0.
p0
ST
short 1
put
E – p0
E
– E + p0
loss
In-the-money
Out-of-money
Bringing Put holder and seller together
Profit
Put (Seller)
ST
-p0
45°
loss
E
Bringing Put holder and seller together
Profit
45°
Put (Seller)
p0
Put (Holder)
45°
loss
E
ST
Example
Consider a call option on £31,250, with option premium at $0.25 per pound (c0=0.25) and
exercise price $1.50 per pound (E=1.5). What is the maximum gain (or loss) on this call option?
Example
Consider a call option on £31,250, with option premium at $0.25 per pound (c0=0.25) and
exercise price $1.50 per pound (E=1.5).
Profit
45°
ST
–$0.25
$1.75
$1.50
loss
Long 1
call on 1
pound
Example
Consider a call option on £31,250, with option premium at $0.25 per pound and exercise price
$1.50 per pound.
Profit
45°
ST
–$7,812.50
31,250×0.25= –7,812.5
loss
Long 1
call on
£31,250
$1.75
$1.50
Example
Consider a put option on £31,250, with premium $0.15 per pound (p0=0.15) and exercise price
$1.50 per pound (E=1.5). What is the maximum gain on this put option?
Profit
Maximum gain per GBP is $1.35/£ =
$1.35
($1.50 – $0.15)/£
ST
–$0.15
$1.35
$1.50
loss
Long 1
put on
£31,250
Example
Consider a put option on £31,250, with premium $0.15 per pound (p0=0.15) and exercise price
$1.50 per pound (E=1.5). What is the maximum gain on this put option?
Profit
Total maximum gain is $42,187.5 =
$42,187.5
£31,250×($1.50 – $0.15)/£
ST
–$4,687.5
$1.35
$4,687.50 = 31,250×0.15
loss
$1.50
Long 1
put on
£31,250
Pricing Relationships at Expiry
• If the call is in-the-money (ie when ST >E) then it is worth ST – E [call option will
be exercised if it is in-the-money]
• If the call is out-of-the-money (ie when ST <E) then it is worth 0 [call option will
NOT be exercised if it is out-of-the-money]
CeT = Max[ST - E, 0]
• At expiration date, an American call option (which has not been previously exercised) is
worth the same as a European option with the same characteristics
CaT = CeT = Max[ST - E, 0]
CaT is the value of the American call at expiration, CeT is the value of European call at
expiration, E is the exercise price per unit of foreign currency, ST is the expiration date spot price.
Pricing Relationships at Expiry
• If the put is in-the-money (ie when ST <E) then it is worth E - ST
• If the put is out-of-the-money (ie when ST >E) then it is worth 0
PeT = Max[E - ST, 0]
• At expiration date, an American put option is worth the same as a European
option with the same characteristics
PaT = PeT = Max[E - ST, 0]
American Option Pricing
• With an American option, you can do everything that you can do with a
European option AND you can exercise prior to expiry date ie for t<T— such
possibility to exercise early has value for holder so that
Cat > CeT = Max[ST - E, 0]
Pat > PeT = Max[E - ST, 0]
Market Value, Time Value and
Intrinsic Value for an American Call
The red line shows the
payoff at maturity of a
call option.
Profit
Long 1
call
Note that even an out-ofthe-money option has
value—as there are still
chances that at some
point in future S becomes
greater than E and option
gets in-the-money.
Intrinsic value
ST
Time value
Out-of-money
loss
In-the-money
E
Example – Hedging FX risk
• Consider a US firm that buys machinery worth of £10 million from a UK
supplier and will pay for such purchasing in one year time. The US firm does
not want any £ exposure and wants to hedge its position.
• Assume that the firm can buy a call option from an investment bank with
- an exercise price of $1.95/£ and
- option premium of $0.02 per £
• The US firm makes the decision to buy the equivalent of £10m in a call option
with an exercise price of $1.95/£ , thus paying an option premium $0.02 ×
£10m = $200,000
• Scenario A: The spot changes to $2.05 before option’s expiration date
• Scenario B: The spot changes to $1.85 before option’s expiration date
Example – Hedging FX risk
Scenario A: The spot changes to $2.05 before option’s expiration date
• The firm (buyer of call and holder of long position) has the right to
exercise its call option at $1.95/£
- it certainly does so and buy £10m at the exercise price of $1.95
- Total cost is $19.500.000 + $200.000 = $19.700.000
• The Investment bank (call option writer/seller and holder of short
position) must buy £ from the market at $2.05 and sell to the firm at $1.95
- Total loss is - $20.500.000 + $19.500.000 + $200.000 = - $800.000
Example
Scenario B: The spot changes to $1.85 before option’s expiration date
• The firm (buyer of call and holder of long position) will not exercise its
right to buy £10.000.000 at $1.95
- instead firm buys it straight from spot market at $1.85
- Total cost is $18.500.000 + $200.000 = $18.700.000
• The Investment bank (call option writer/seller) does nothing and cashes
in the option premium
- Profits are $200.000
Example
• The call option helps US firm limit the cost of £10.000.000 to a max of
$19.700.000
- ie strike price + premium → $1.95 + $0.02 for each GBP bought
• Firms with open positions in £ may use FX options to cover such positions
Exercises
What is meant by the terminology that a FX call option is in-the-money?
a. It means that St > E
b. It means that E > St
c. It means that St = E
d. None of the above is correct
Exercises
What is meant by the terminology that a FX call option is in-the-money?
a. It means that St > E
b. It means that E > St
c. It means that St = E
d. None of the above is correct
Exercises
Consider the lower boundary formula for the European FX call option. This
formula posits that the call premium will increase
a. The wider the difference St-E
b. The wider the difference E-St
c. Every time E is greater than 0
d. None of the above
Exercises
Consider the lower boundary formula for the European FX call option. This
formula posits that the call premium will increase
a. The wider the difference St-E
b. The wider the difference E-St
c. Every time E is greater than 0
d. None of the above
Exercises
Assume your firm based in San Francisco is due to pay 32,250 GBP in three
months time to a supplier based in the UK. Assume also that you expect
S($/£) to increase – ie $ to depreciate against £ in the coming three months and that you want to hedge against the risk of depreciation. What options are
available to you?
a. Buy today a FX Call option with expiration date in 3 months
b. Exchange dollars for GBP in three months time right before the delivery of
the payment
c. Buy today a FX Put option with expiration date in 3 months
d. None of the above is correct.
Exercises
Assume your firm based in San Francisco is due to pay 32,250 GBP in three months
time to a supplier based in the UK. Assume also that you expect the S($/£) to
increase – ie $ to depreciate against £ in the coming three months - and that you want
to hedge against the risk of depreciation. What are options available to you?
a. Buy today a FX Call option with expiration date in 3 months
b. Exchange dollars for GBP in three months time right before the delivery of the
payment
c. Buy today a FX Put option with expiration date in 3 months
d. None of the above is correct.
Exercises
Assume your firm based in San Francisco is due to receive a payment of 32,250 GBP in
three months time from a client based in the UK. Assume also that you expect the
S($/£) to depreciate in the coming three months. What is the best option available to
you?
a. Buy today a FX Call option with expiration date in 3 months
b. Exchange GBP for dollars in three months time right after the delivery of the
payment
c. Buy today a FX Put option with expiration date in 2 months
d. None of the above are feasible options.
Exercises
Assume your firm based in San Francisco is due to receive a payment of 32,250 GBP in
three months time from a client based in the UK. Assume also that you expect the
S($/£) to depreciate in the coming three months. What is the best option available to
you?
a. Buy today a FX Call option with expiration date in 3 months
b. Exchange GBP for dollars in three months time right after the delivery of the
payment
c. Buy today a FX Put option with expiration date in 2 months
d. None of the above are feasible options.
Notes on options
• Currency option, being the right to buy or sell a known amount of foreign
currency at an agreed-upon price.
• This is much more flexible instrument than a forward or futures contract.
• Once the option has been bought, it can always be sold in the secondary market.
The market price can never drop below ZERO. Nor can the price drop below the
value of a comparable forward contract.
• The holder of the option is prepared to pay the premium because the option acts
as an insurance contract, that is, once can obtain insurance against the possible
depreciation of a foreign currency buy buying a put, while a call option offers
insurance against a possible appreciation.
284
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