Introduction to FX market
Chapter 2.1, 2.2, and 2.4
BUSINESS
SCHOOL
Useful resources
› Additional reading folder on BB.
› Recommended website:
- http://www.oanda.com/
- Yahoo Finance
- http://www.igmarkets.com.au/
- http://www.travelex.com.au
- A video introduction:
- https://www.youtube.com/watch?v=tAKL3g2bM-E
2
Going to US for a holiday now? Extra costs?
3
How much extra?
4
What is the FX market?
› FX market: the global market in which national currencies are bought
and sold against one another, and where exchange rates determined.
› Daily trading volume in the foreign exchange (FX) market is immense:
- In 2019 average daily trading volume or turnover in the FX market was
estimated at 6.6 trillion USD!
- One day’s FX trading volume is comparable to one month’s trading
in NYSE
5
The Organization of the Foreign Exchange Market
› The foreign exchange market is an over-the-counter (OTC) market:
- There is no one physical location or organised exchange where traders
get together to exchange currencies.
- Rather, the FX market consists of a complex international network of
informal linkages between key market participants communicating with
each other via telephone, fax, e-mail etc.
- The FX market is 24-hour market; trading in FX virtually never ceases
except for weekends.
› The foreign exchange market operates around the clock, from its “open” at
6:00am Sydney time on Monday morning until the “close” at 5:00pm New
York time on Friday.
6
Exhibit 2.1 The Structure of the Foreign Exchange
Market
Most important cities:
London
New York
Tokyo
ForEx (or FX)
operates 24 hrs/day
Interbank market –
50% of transactions
Corporations – 13.4%
Other financial
institutions – 48%
Most trades are $1M
or more!
7
Geographic Extent of the Market
Measuring FOREX Market Activity: Average Electronic Conversions per Hour
8
Function of FX market
› Foreign Exchange Markets
› The FX market provides the physical and institutional structure through
which
› The money of one country is exchanged for that of another country
› The rate of exchange between currencies is determined
› Foreign exchange transactions are physically completed
› A foreign exchange transaction is an agreement between a buyer and a
seller that a fixed amount of one currency will be delivered for some other
currency at a specified rate.
9
The Foreign Exchange Market
› Most of the trading takes place in just a handful of key
currencies. (USD, Euro, Yen, UK Pound, CHF, CAD,
AUD)
› A few key financial centers account for the bulk of daily
trading volume in foreign exchange (UK, US, Japan,
Singapore)
› See the BIS 2019 survey
› https://www.bis.org/statistics/rpfx19_fx.pdf
10
Foreign Exchange Market Transactions
› Foreign exchange market permits transfers of purchasing power
denominated in one currency to another.
› Interbank market – wholesale market in which major banks trade with
one another. Accounts for ~95% of foreign exchange transactions.
Spot market – where currencies are traded for immediate
delivery (30% in 2019)
Forward market – where contracts are made to buy or sell
currencies for future delivery (15% in 2019)
Swap transactions – involve a package of a spot and a forward
contract (49% in 2019)
Derivatives including currency swaps, options etc.(<10% in
2019)
11
How liquid is the Foreign exchange market?
› Liquidity
- Ease with which one can sell an asset AT ITS FAIR VALUE
- Low transaction costs
› Quoted prices change as often as 20 times a minute.
› It is estimated that the world’s most active exchange rate can
change up to 18,000 times during a single day.
12
Fx market participants
› Foreign exchange dealers
- Who are they?
- Commercial banks
- Investment banks
- Market makers – they make it easier for buyers and sellers to come
together
› Foreign exchange brokers
› Brokerage firms (intermediary – does not put own money at risk)
› Other participants in the forex market
- Central banks
- Multinational corporations
13
Key FX Market Participants
› CUSTOMERS or CLIENTS.
- Companies & individuals wishing to buy and sell FX in order to
finance foreign trade and international investment operations.
(Exporters, importers, tourists, immigrants, investors).
- ‘Price-takers’ in FX market
ie buy/sell currencies at prices (exchange rates) determined by
the market makers in FX market.
14
Key FX Market Participants
› BANK and NON-BANK FX DEALERS.
- Market-Makers in FX Market (Price-makers);
- Stand ready to buy and sell currencies at (bid and offer) exchange
rates they quote, via their FX dealers.
- Deal in retail (ie with ‘Customers’) and wholesale or “interbank”
markets.
- Take positions; engage in FX arbitrage & speculation.
15
Key FX Market Participants
› SPECULATORS AND ARBITRAGEURS.
- Speculators and arbitragers seek to profit from trading in the
market itself
- They operate for their own interest, without need or obligation to
serve clients or ensure a continuous market
- Speculators seek all their profit from exchange rate changes
- Arbitragers try to profit from simultaneous differences in exchange
rates in different markets
- A large proportion of speculation and arbitrage is conducted on
behalf of major banks by traders employed by those banks.
16
Key FX Market Participants
› FX BROKERS.
- Foreign exchange brokers are agents who facilitate trading
between FX dealers without themselves becoming principals in
the transaction
- Disseminate market information and bring together buyers &
sellers with matching needs.
- Accepts Limit orders - orders placed with brokers by banks to
buy/sell a certain quantity of foreign currency at a pre-specified
price. Broker puts these on its “books” and attempts to match
purchase orders with sell orders
- Do not deal or take positions in foreign exchange. They receive
commissions on deals that they broker in interbank FX market.
17
Key FX Market Participants
› CENTRAL BANKS AND TREASURIES
- Central banks and treasuries use the market to acquire or spend
their country’s currency reserves as well as to influence the price at
which their own currency trades
- Act as bankers for their governments in meeting FX requirements.
- Sometimes intervene in FX market to “smooth” exchange rate fluctuations
and/or to prevent domestic currency from appreciating or depreciating
excessively.
18
What is special about Foreign Exchange Market?
› The competitive marketplace
- No product differentiation – money is money
- Has been a lot of players
- Recently, there has been consolidation:
- Top 5 account for around 50%
- Deutsche Bank, UBS, Citigroup, Barclays and J.P. Morgan Chase
- Top 20 over 90%
- Still exceedingly competitive with no signs of any clear leader in this market
19
Inside the Interbank Market II: Communications and
Fund Transfers
› Communication systems
• Society of Worldwide Interbank Financial Telecommunications
(SWIFT) – links more than 7500 banks in 200 countries
• Clearing House Interbank Payments System (CHIPS) – clearing
house in U.S. for dollars
• Fedwire – links computers of more than 7500 institutions that have
deposits with the U.S. Federal Reserve
• Trans-European Automated Real-time Gross Settlement Express
Transfer (TARGET) – Euro counterpart to Fedwire
20
Communication Systems in the Forex Market
21
Inside the Interbank Market II: Communications and Fund
Transfers
› Cross-currency settlement (or Herstatt) risk
• The risk that a financial institution may fail to deliver on one
side of a foreign exchange deal though the counterparty to
the trade as delivered its promised payment
• How this risk is addressed
-
First, banks now have strict limits on the amount of transactions they
are willing to settle with a single counterparty on a given day
-
Second, banks have started to engage in a variety of netting
arrangements
22
Exhibit 2.10 Netting Arrangements
23
Exhibit 2.10 Netting Arrangements (cont.)
24
How are currencies quoted?
› Exchange rate – price of one currency in terms of another
•
JPY100 = USD1; ¥100 = $1
•
¥100/$1 or ¥100/$ (the number one is implied)
•
http://www.oanda.com/
› Direct vs. Indirect quotation; American vs. European
quotation
•
Direct – quoting 1 unit of foreign currency in terms of domestic currency
•
Indirect- quoting 1 unit of domestic currency in terms of foreign currency
•
Use $ to describe value of one unit of £ (or others) : $1.60 = £1; this is
called the American quote
•
Use £ (or others) to describe value of one unit of $: $1 = £0.625; often
called European quote
25
Currency Quotes and Prices
› Direct and indirect are inverse: Direct = 1/Indirect
› American and European quotations are also inverse
26
Are these rates direct or indirect quotations?
https://www.rba.gov.au/statistics/frequency/exchange-rates.html
27
The Exchange Rate and its Quotation
› Every bilateral exchange rate treats one currency as the item
or commodity/base which is being priced, with the other
currency as the units in which its price is measured (“terms”
or “quote”).
› AUD=USD 0.7205, the Australian dollar is the “base”
currency and US dollar is the “terms” currency.
› the choice of commodity currency is entirely arbitrary. We
could also do:
› USD1 = AUD 1.3879

(AUD1 = USD 0.7205)
28
A Point of Clarification
› In this class, we use a convention:
› S(USD/AUD) reads “the number of US dollars per Australian dollar”.
The slash symbol “/” stands for “per” in the same way that for example
“km/hr” reads “kilometers per hour”.
Thus, for example, the quote S(USD/AUD) = 0.7515 reads as “0.7515
US dollars per Australian dollar”.
› All of the following are identical interpretations of this exchange rate
quotation:
0.7515 USD exchanges for 1 AUD
0.7515 USD = 1 AUD
1 AUD exchanges for 0.7515 USD
1 AUD = 0.7515 USD
› *However, it is not always the case that the currency in
denominator is the commodity currency! For example: Oanda
quotation
29
The Exchange Rate and its Quotation
› It is always important to understand which currency is
commodity currency and which one is terms currency
when dealing with an exchange rate
› Let S(i/j)
= spot price of currency j expressed in units of currency i.
= no. of units currency i per unit of currency j.
 j is the commodity currency, i is the terms currency.
› e.g AUD = 0.7205 USD  S(USD/AUD) = 0.7205.
Currency i is the US dollar (terms currency);
currency j is the Australian dollar (commodity currency)
30
The Exchange Rate and its Quotation
› ↑S(i/j)  appreciation of currency j (relative to i )
(appreciation of “commodity” currency)
›  S(i/j)  depreciation of currency j (relative to i )
(depreciation of the commodity currency)
› e.g if St (USD/AUD) = 0.7205 and St-3(USD/AUD) = 0.7109
then Australian dollar is said to have appreciated 1.35%
[100*(0.7205-0.7109)/(0.7109) = 1.35%] against the US dollar over the 3day period.
› How much did US$ depreciated against the A$?
31
Describing changes in exchange rates
›
(new value - old value)
100 
old value
What about if quote is S(£/$)?
32
Get familiar with those currency symbols
Exhibit 2.4 Currencies and Currency Symbols
33
Wrap up
› This week :
› What is the Foreign Exchange Market?
› Organization
› Size and Function
› Participants
› Quotations of currencies
› Next week:
› Two-way quotations and cross rates
› Arbitrage in currency market
› Forward and swap markets
34
Exchange rate quotations and arbitrage
Chapter 2.2, 2.3, and 2.5
BUSINESS
SCHOOL
Where are we up to?
› Last week :
› What is the Foreign Exchange Market?
› Organization
› Size and Function
› Participants
› Quotations of currencies
› This week:
› Two way quotations and cross rates
› Arbitrage in currency market
› Forward and swap markets
2
Currency Quotes and Prices
• Vehicle currencies and currency cross-rates
• Vehicle currency – a currency that is actively used in many
international financial transactions around the world
•
Used due to transaction costs of making markets in certain
currencies being too high
•
U.S. Dollar primary vehicle currency (89% of all transactions)
• Cross-rates
• Trading currency in the New York market where both
currencies are not expressed in U.S. dollars
•
Trend toward cross-rate transactions
3
Exhibit 2.6 Representative Cross-Rate Quotes
4
The Exchange rate and its Quotation
› In foreign exchange quotations, the units of measurement follow the
usual rules of algebra.
› e.g
j/i = 1  (i/j)
AUD/USD = 1  USD/AUD
› If S(i/j) = a units of i, then S(j/i) = 1  S(i/j) = 1/a
units of j
i.e If a units of currency i exchange for one unit of currency j, then it
must be the case that 1/a units of currency j must exchange for one
unit of currency i.
› e.g
if S(USD/AUD) = USD 0.6330,
 S(AUD/USD) = 1  (USD 0.6330)
= AUD 1.5798
5
Cross Exchange Rates
› Cross exchange rates are exchange rates between currencies when
neither of the 2 currencies is the US dollar e.g S(JPY/AUD),
S(EUR/GBP), S(CHF/NZD) etc.
› Recall that units of measurement follow the rules of algebra.
If we have three currencies currency i, currency j
and currency z, then:
S (i / z )
S (i / j ) =
S ( j / z)
S(i / j) = S(i / z)  S(z / j)
› e.g
S ( EUR / AUD ) =
S ( EUR / USD)
S ( AUD / USD)
S ( EUR / AUD ) = S ( EUR / USD)  S (USD / AUD )
6
Cross Exchange Rates
› Question: If S(EUR/USD) = 1.7500 and S(USD/AUD) = 0.7000, what
is the implied cross exchange rate quotation for the Australian dollar
expressed in units of Euro (EUR)?
› Answer:
We need to determine S(EUR/AUD).
› However we know: S(EUR/AUD)=S(EUR/USD)* S(USD/AUD)
= 1.75*0.7 = 1.2250 EUR
›
S(EUR/AUD) = EUR 1.2250 
AUD1 = EUR1.225
i.e If 1 AUD buys USD 0.7000 and 1 USD buys EUR1.7500, then 1
AUD will buy 1.225 EUR (= 0.7000 x 1.7500)
7
Cross Exchange Rates
› Question: If S(USD/GBP) = USD 1.8750 and S(USD/AUD)
= USD 0.7250, what is the price of British pound (GBP) in terms of
Australian dollars?
› Answer:
We need to determine S(AUD/GBP).
› We know:
S(USD/GBP)/ S(USD/AUD) = S(AUD/GBP)
› 1.8750/0.7250=2.5862
›

S(AUD/GBP) = AUD 2.5862 
GBP1 = AUD2.5862
8
Currency Quotes and Prices
› Triangular arbitrage
• An arbitrage process involving three currencies
• Keeps cross-rates in line with exchange rates quoted relative to the
U.S. dollar
• Occurs when one can trade three currencies and make a profit
(versus two)
1. EUR1.4381/GBP
2. EUR0.8408/USD
3. USD1.7395/GBP
9
Exhibit 2.7
Triangular Arbitrage Diagram
1. EUR1.4381/GBP
2. EUR0.8408/USD
3. USD1.7395/GBP
From 1 &2
USD1.7104/GBP
Should sell GBP for USD
10
Exhibit 2.8
Good and Bad Triangular Arbitrages
1.EUR1.4381/GBP
2.EUR0.8408/USD
3. USD1.7395/GBP
11
Spot Bid and Offer Exchange Rate Quotes
›
In inter-bank spot FX market, when dealers provide an exchange rate
quotation, they will typically give a “two-way” price i.e the buying price
and the selling price of the commodity currency. For example:
S(USD/AUD) = 0.6504-09
› AUD is the commodity currency; USD is the terms currency.
› What this quote means is that the dealer will either:
Buy AUD in exchange for USD
@ 1AUD = USD 0.6504
Sell AUD in exchange for USD
@ 1 AUD = USD 0.6509
12
Reciprocal Nature of Bid and Ask Exchange Rates
› Bid price: S(JPY/USD) = 110.25
› Ask price: S(JPY/USD) = 110.30
› Q. Bid-ask price for S(USD/JPY)?
› Bid S(USD/JPY) = 1/110.30 *100= 0.9066 (per 100 JPY)
› Ask S(USD/JPY) = 1/110.25*100 = 0.9070(per 100 JPY)
13
Exhibit 2.8 The Reciprocal Nature of Bid and Ask
Exchange Rates
14
Spot Bid and Offer Exchange Rate Quotes
›
15
2.3 Inside the Interbank Market I: Bid-Ask Spreads
and Bank Profits
Treasurer of a U.S. company purchases pounds with dollars to hedge
a British goods purchase. Directly after, he is told that they no longer
need to purchase the goods. He then sells the pounds back for
dollars.
Assume that the bid-ask spread is 4 pips. If the ask rate is $1.50/£,
the bid rate is $1.4996/£ and the percentage spread using mid-point
price is:
[($1.50/£) – ($1.4996/£)]/($1.4998/£) = 0.03%
If the treasurer bought £1M at $1.50/£, the cost would have been:
£1M * ($1.50/£) = $1.5M
Selling back: £1M * ($1.4996/£) = $1,499,600, or a loss of $400 on the
two transactions – 0.03% of $1.5M
16
2.3 Inside the Interbank Market I: Bid-Ask Spreads and
Bank Profits
› Magnitude of bid-ask spreads
- Interbank market
- Typically less than 10 pips (fourth decimal point in a currency quote)
- 0.05% - 0.07% for major currencies
- Lower for extremely liquid currencies like U.S. dollar (i.e., 1 pip for $/€
exchange rate quote)
- Higher for less liquid currencies
- Physical exchange
- Can be large at 5% or more (in the tourist market)
- Banks have to have inventory, which means it is not interest bearing
- Banks must transact with brokers
- Online trading Web sites provide competitive spreads
- Use credit cards to exchange when in another country – this is the best
possible rate for you!
17
Spot Bid and Offer Exchange Rate Quotes
› When dealing in foreign exchange, if you ‘buy’ one currency you also
necessarily ‘sell’ the other currency and vice versa.
› For example, the quote on a AUD 5 million parcel of S(USD/AUD) =
0.7650 - 80 means that the dealer will:
Buy AUD 5 million @ 1 AUD =0.7650,  simultaneously sell USD
3,825,000 (= 5,000,000 x 0.7650)
Sell AUD 5 million @ 1 AUD = 0.7680,  simultaneously buy USD
3,840,000 (= 5,000,000 x 0.7680)
18

Spot Quotations, continued
⚫
Quotes are given in pairs that reflect the bid-ask price.

E.g., pound sterling is quoted at $1.9719-28.

$1.9719 is the (bid) rate at which banks will buy pounds

$1.9728 is the (ask) rate at which banks will sell pounds

The spread equals the dealer’s profit

⚫
The bid-ask spread is often quoted by the last two numbers; e.g.,
19-28.
Bid-ask quote expressed in American and European terms and as
direct and indirect quotes:
American Terms
Direct in U.S.
Indirect outside
U.S.
European Terms*
Direct outside U.S.
$1.9719-28
Indirect in U.S.
(1/$1.9728)(1/$1.9719)
=£0.5069-71
*Note that the bid and ask prices are reversed in quoting in European terms.
19
Working with two-way quotations:
› Basically, there are 2 simple steps in the determination of bid
and offer cross exchange rate quotations from two other
bilateral bid and offer exchange rate quotes.
› Determine whether you have to multiply or divide the two
exchange rate quotations.
› In determining which combination of bid and offer rates to use,
recognize that dealer will always want to have the bid price of
the commodity currency as low as possible, and the offer
price of the commodity currency as high as possible.
20
Two rules
› Keep track of your currency units.
› Think of buying or selling the currency in the denominator of a foreign
exchange quote.
21
Spot Bid and Offer Cross-Rate Quotes
› Example 1:
› If S(Yen/USD) = 123.00-10 and S(USD/AUD) = 0.7000-05, what is
the cross-rate quotation on the S(Yen/AUD)?
Answer:
1. S(Yen/AUD)=S(YEN/USD)*S(USD/AUD)
2. Sb(Yen/AUD)=Sb (YEN/USD)*Sb (USD/AUD)
----Bid price as lower as possible
3. Sa(Yen/AUD)=Sa(YEN/USD)*Sa (USD/AUD)
----Ask price as higher as possible
4. S(Yen/AUD) = 86.10 - 23
›
S(Yen/AUD) = 86.10-23
22
Spot Bid and Offer Cross-Rate Quotes
› Example 2:
› If S(USD/AUD) = 0.7000-05 and S(USD/GBP) = 1.5550-60, what is
the cross-rate quotation S(GBP/AUD)?
Answer:
1. S(GBP/AUD) = S(USD/AUD)/S(USD/GBP)
2. Sb(GBP/AUD) = Sb (USD/AUD)/Sa(USD/GBP) = 0.7/1.5560
----Again bid price as lower as possible
3. Sa(GBP/AUD) = Sa (USD/AUD)/Sb(USD/GBP) = 0.7005/1.5550
----Again ask price as higher as possible
S(GBP/AUD) = 0.4499-0.4505
23
Forward Markets and Transaction Exchange Risk
Chapter 3.1, 3.3, 3.4, and 3.5
BUSINESS
SCHOOL
Transaction Exchange Risk
› Fancy Foods, a U.S. company imports meat pies from British
firm. FF has to pay £1,000,000 in 90 days in return for
supplies. The spot rate (current exchange rate) is $1.50/£.
How many dollars will Fancy Foods have to pay?
› The answer depends on exchange rate in 90 days
- If exchange rate in 90 days is $1.53/ £,
($1.53/ £)*(1,000,000)=$1,530,000 should be paid
- If exchange rate in 90 days is $1.46/ £,
($1.46/ £)*(1,000,000)=$1,460,000 should be paid
› Since an exchange rate in future is NOT known, Fancy Foods
faces risk/uncertainty
25
Transaction Exchange Risk
› Transaction exchange risk – possibility of taking a loss in
foreign exchange transactions
› Who incurs transaction exchange risk?
• Corporations
• Institutional investors
• Individuals
› How to avoid?
• Hedging – get rid of uncertainty by using derivatives
26
Forward Contract
› Forward contract: An agreement to buy (long position) or sell
(short position) an asset (underlying asset) at a future time
(maturity) for a certain price (forward price)
› Example: Agree to buy a gold in 30 days at $300
- Long position , underlying asset = gold
- maturity = 30days , forward price = $300
› Underlying assets can be individual stock (IBM), stock market
index (S&P 500), foreign currency, interest rate, weather, etc
› Forward FX contract
- Example: Agree to buy USD 1 million in 90 days at the forward exchange
rate of 1.4 AUD / USD
› Note that forward exchange rate is agreed (determined) today
27
Hedging Transaction Exchange Risk
› Fancy Foods can hedge transaction exchange risk
› Fancy Foods enters into a forward contract:
- agrees today to buy £1,000,000 in 90 days at the forward
exchange rate of $1.53/£
- Fancy Foods will pay $1,530,000 whatever exchange rate in
90 days will be
- No exchange rate risk!
Day
0
e0 = $1.50/ £
90
e90 : unknown
Exchange risk
f90 = $1.53/ £
No exchange risk:
£1,000,000 = $1,530,000
28
Hedging Transaction Exchange Risk
› Q. Does hedging always yield a better outcome?
- If e90 > $1.53/ £, hedging turns out to be a good choice (Ex
post)
- Suppose that e90 = $1.60/ £. Without hedging, FF pays
$1.60M. By hedging, FF pays only $1.53M. It pays less
than the market price
- If e90 < $1.53/ £, hedging turns out to be a bad choice (Ex
post)
- Suppose that e90 = $1.50/ £. Without hedging, FF pays
$1.50M. For hedging, FF pays $1.53M! It pays more than
the market price
› Answer) Hedging position can yield either better or worse
position compared to no hedging position
29
Hedging Transaction Exchange Risk
› The costs and benefits of a forward hedge
- Ex-ante: eliminate/reduce exchange rate risk
- Ex-post: Hedged positions turns out to be either gain or loss
depends on the relationship between exchange rate in future and
forward exchange rate
30
The Forward Foreign Exchange Market
› Forward contract maturities and value dates
• Forward value or settlement date
-
Most active dates are 30, 60, 90, 180 days
-
Highly customizable
-
Exchange takes place on the forward value date
› Forward bid/ask spreads
• Larger than in spot market
• Spreads higher for greater maturities
• 0.10% for major currencies
• 90 day: 15% greater than spot contracts
31
Foreign Exchange Swap Transactions
› A transaction involving the sale/purchase of a currency today
combined with an offsetting purchase/sale of the same
currency at some future point in time.
› FX swap typically consists of two “legs” - a spot FX transaction and
offsetting forward FX transaction.
› For example:
- Day 1: Sell AUD/buy USD @ spot exchange rate (spot leg)
- Day 90: Buy AUD/sell USD @ fwd exchange rate (fwd leg)
- Sell today $10m AUD (buy USD)@ spot exchange rate of
$0.6500 USD and agree to buy back in 2 weeks time $10m AUD
(sell USD) at the forward exchange rate of 0.6510 USD
32
Exhibit 3.7 Cash Flows in a Spot-Forward Swap
S: 104.3 – 104.35¥/$
F: 104.1- 104.20 ¥/$
• Nomura: dealer, IBM: customer/client
33
Forward Premiums and Discounts
› Forward premium - occurs when the price of the
currency contract is higher than the spot rate
•
F$/€ > S$/€ (the price of a € is higher for Forward)
› Forward discount - occurs when the price of the
currency contract is lower then the spot rate
•
F$/€ < S$/€ (the price of a € is lower for Forward)
forward − spot
360
AnnualizedPercent =

spot
Ndays
•
ex) For 2% premium during 90 days: 2% x 360/90 = 8% p.a
34
Forward Rates and FX Swap points
› Forward exchange rate quotations are quoted in a similar manner to
spot prices.
› A two-way bid/offer spread is quoted with the commodity currency
again being the currency referred to as being “bought” or “sold” in a
transaction.
› There are two ways of quoting forward rates.
› First, the outright forward exchange rate is expressed as exactly as
the spot exchange rate, using two numbers to represent the bid and
offer forward rates.
- The forward market is less liquid than the spot
- Banks are exposed to counterparty default risk
- Most of the forward contracts happens in the swap market
35
Swap market
› Second, forward rate can be quoted using a spot
rate and the swap points, which is the swap rate
(also known as forward points) of discount or
premium.
› e.g An FX dealer may quote the following
S(USD/AUD) rates:
Spot
0.7000-05
3-month swap points
40/38
(3-month forward points)
36
Forward Rates and FX Swap points
› The forward price is an adjustment (represented by the swap
or forward points) to the spot rate to give what is known as
the outright forward rate.
› The outright forward rate is the predetermined exchange rate
at which an FX transaction is settled at a future date.
› In this example, the 3-month forward S(USD/AUD) bid rate is
0.6960 (= 0.7000 - 0.0040) and the corresponding offer rate
is 0.6967 (= 0.7005 - 0.0038).
37
Forward Rates and FX Swap points
› In this example we obtain the 3-month outright forward rate by
subtracting the 3-month “swap points” from the bid and offer quotes of
the spot exchange rate.
› Adding or Subtracting Swap points?
› Rule:
If the left-hand side of swap point quotation(bid) is greater than the
right-hand side of the swap point quotation (offer), you SUBTRACT
the swap points from the spot rate to obtain the outright forward rate.
If the L.H.S. of swap point quotation is less than the R.H.S. of the
swap point quote, you ADD the swap points to spot rate quotation.
38
Forward Rates and FX Swap points
› If we have the following quotations swap points:
3-month swap USD/AUD 40/38 (subtract swap points from spot)
3-month swap CAN/USD 15/20 (add swap points from spot)
› and the following spot rate quotations
S(USD/AUD) = 0.7000-05
S(CAN/USD) = 1.2015-25
then we have following outright 3-month forward rates:
› 3-month F(USD/AUD) =
3-month F(CAN/USD) =
39
Forward Rates and FX Swap points
› Forward Premium (Discount):
If outright forward exchange rate is greater than (less than) spot
exchange rate.
› If F(USD/AUD) > S(USD/AUD)
 Australian currency is at a forward premium.
› If F(USD/AUD) < S(USD/AUD)
 Australian currency is at a forward discount.
› If “commodity’ currency is at a forward premium (discount) then
“terms” currency must be at a forward discount (premium).
› If swap bid points are greater (less) than swap offer points, then:
(a) commodity currency is at forward discount (premium) (b) terms
currency is at forward premium (discount)
40
Forward Rates and FX Swap points
› Next Week:
› What determines the forward price?
› the spot rate
› the term or maturity of the forward contract
› the respective nominal interest rates of the two currencies in the
exchange rate quotation.
› Once we know these, we can calculate the swap or forward points and
hence the forward exchange rate.
41
Practice 1
› Dealer A quotes 1.0030–1.0045 for the USD/AUD exchange rate to dealer B.
What are the following:
› (a) The price at which A is willing to buy the Australian dollar? 1.0030 $/A$
› (b) The price at which A is willing to buy the US dollar? 1.0045 $/A$; 1/1.0045
A$/$
› (c) The price at which B can buy the Australian dollar? 1.0045 $/A$
› (d) The price at which B can buy the US dollar? 1.0030 $/A$ or inverse
› (e) The price at which A is willing to sell the Australian dollar? 1.0045 $/A$
› (f) The price at which A is willing to sell the US dollar? 1.0030 $/A$ or inverse
› (g) The price at which B can sell the Australian dollar? 1.0030 $/A$
› (h) The price at which B can sell the US dollar? 1.0045 $/A$ or inverse
42
Practice 2
› Dealer A quotes 1.3530–1.3580 for the SGD/AUD exchange
rate to dealer B. What are the following:
› (a) How much SGD is A willing to pay for 1m AUD?
- 1.3530S/A *1m A= 1,353,000 SGD
› (b) How much AUD is A willing to pay for 1m SGD?
- 1.3580S/A
- 1m S/1.3580 = 736377 AUD
› (c) How much SGD B is willing to pay for 1m AUD?
- 1.3580S/A *1m a = 1,358,000 SGD
› (d) How much AUD B is willing to pay for 1m SGD?
- 1.3530S/A
- 1M/1.3530 = 739098.3 AUD
43
The interest parity conditions I - CIP
Chapter 6.1, 6.2, and 6.3
BUSINESS
SCHOOL
Where are we up to?
› Last week :
› Two way quotations and cross rates
› Arbitrage in currency market
› Forward and swap markets
› This week:
› Arbitrage activities around interest rates differences across currencies
› Interest rate parity condition
2
Interest rate Parity Conditions
› Interest rate parity provides the link between FX markets and international
money markets.
› Interest rate parity presents the difference in nominal interest rates is
equal to, but opposite in sign to, the forward premium.
3
Covered Interest Parity (CIP)
Covered Interest Parity (CIP) describes an equilibrium
relationship between the spot exchange rate, the
forward exchange rate, and nominal domestic and
foreign interest rates.
Assumptions underlying CIP:
› There are no capital mobility restrictions across national boundaries
- perfect capital mobility.
› No transaction costs.
› No taxes
4
Covered Interest Parity (CIP)
› Consider the following notation:
iUS = annual nominal interest rate on a US-dollar denominated asset
iAUS = annual nominal interest rate on an Australian-dollar denominated
asset
S(USD/AUD) = spot exchange rate; no. of US dollars per Australian dollar
F(1 yr)(USD/AUD) = 1-year forward exchange rate
5
Covered Interest Parity (CIP)
Covered Interest Parity (CIP):
(US investor’s perspective)
(1 + iUS ) =
F(1 yr ) (USD / AUD)
S (USD / AUD)
(1 + i AUS )
OR, equivalently:
(Australian investor’s perspective)
S (USD / AUD)
(1 + i AUS ) =
(1 + iUS )
F(1 yr ) (USD / AUD)
6
Covered Interest Parity (CIP)
› How is the covered interest parity (CIP) condition derived?
› Suppose that a US investor has initially a certain amount of
US dollars and is deciding whether to invest these funds in
either of the following two investment options:
› (i) A US-dollar denominated asset paying an annualised
nominal interest rate of iUS.
› (ii) An Australian-dollar denominated asset paying an
annualised nominal interest rate of iAUS
7
Covered Interest Parity (CIP)
› Investment option (i): Invest in US dollar denominated
asset:
- For each 1 US dollar invested in the US-dollar denominated asset, the
investor will receive, after one year, $US1(1 + ius)
› Investment option (ii): Invest in Australian dollar
denominated asset
- For each 1 US dollar, the investor can obtain on the spot FX market
[1/S(USD/AUD)] Australian dollars.
- If this quantity of Australian dollars is invested in the Australian-dollar
denominated asset, the investor will have at the end of one year
[1/S(USD/AUD)]x(1 + iAUS) Australian dollars.
8
Covered Interest Parity (CIP)
› Investment option (ii):
- Foreign exchange risk is present; the certain number of Australian
dollars received at the end of the 1-year investment horizon
represents an uncertain amount of US dollars.
- If at the time when the funds are initially invested in the Australian
asset, the investor also enters into a forward FX contract to sell
Australian dollars 1-year forward, at a price given by
F(1 yr)(USD/AUD), the investor will be able to guarantee the number of
US dollars he/she will receive.
9
Covered Interest Parity (CIP)
› Investment option (ii):
- Thus with foreign exchange risk covered, for every 1 US dollar invested in
the Australian-dollar denominated asset, the investor will obtain at
maturity (i.e., after one year) the following number of US dollars from
his/her investment in the Australian asset:
$US1{F(1 yr)(USD/AUD)x[1/ S(USD/AUD)]x(1 + iAUS)}
or
 F(1 yr ) (USD / AUD)

$US1
(1 + i AUS ) 
 S (USD / AUD)

10
Covered Interest Parity (CIP)
› Which investment option should the investor choose?
› Compare the US gross dollar return from the two
investment alternatives
› i.e. gross $US return from US asset vs gross covered $US
return from Australian asset
(1 + iUS )
vs
F(1 yr ) (USD / AUD )
S (USD / AUD )
(1 + i AUS )
11
Covered Interest Parity (CIP)
› Choose US-dollar denominated asset (option (i)) if:
(1 + iUS )

F(1 yr ) (USD / AUD)
S (USD / AUD)
(1 + i AUS )
gross $US return from US asset > gross covered $US return from Australian asset
› Choose Australian-dollar denominated asset (option (ii)) if:
(1 + iUS )

F(1 yr ) (USD / AUD)
S (USD / AUD)
(1 + i AUS )
gross $US return from US asset < gross covered $US return from Australian asset
12
Covered Interest Parity (CIP)
› Investor will be indifferent between US-dollar and Australian-dollar
denominated assets when:
(1 + iUS )
=
F(1 yr ) (USD / AUD)
S (USD / AUD)
(1 + i AUS )
gross $US return from US asset = gross covered $US return from Australian
asset
› When investor is indifferent between the two assets, we have
Covered Interest Parity (CIP):
(1 + iUS )
=
F(1 yr ) (USD / AUD)
S (USD / AUD)
(1 + i AUS )
13
Covered Interest Parity (CIP)
› This is CIP from perspective of US investor ie
Gross return on “domestic” USD-denominated asset (LHS)
= gross covered USD return on “foreign” AUD-denominated asset (RHS)
(1 + iUS )
=
F(1 yr ) (USD / AUD)
S (USD / AUD)
(1 + iAUS )
› CIP from perspective of Australian investor:
Gross return on “domestic” AUD-denominated asset (LHS)
= gross covered AUD return on “foreign” USD-denominated asset (RHS)
S (USD / AUD)
(1 + i AUS ) =
(1 + iUS )
F(1 yr ) (USD / AUD)
14
Covered Interest Parity (CIP)
› CIP relationship underpins the determination of the forward exchange
rate.
› Re-arranging the CIP relationship we can write:
F(1 yr ) (USD / AUD)
=
(1 + iUS )
S (USD / AUD)
(1 + i AUS )
› Forward exchange rate is thus determined by:
- spot exchange rate
- respective nominal interest rates of the two currencies in the exchange rate
quotation
- term or maturity of forward FX contract
15
Covered Interest Parity (CIP)
› Re-arranging the CIP expression we obtain:
F(1 yr ) (USD / AUD )
S (USD / AUD )
=
(1 + iUS )
(1 + iAUS )
F(1 yr ) (USD / AUD ) − S (USD / AUD )
S (USD / AUD )
F(1 yr ) (USD / AUD ) − S (USD / AUD )
S (USD / AUD )
=
(iUS − iAUS )
(1 + iAUS )
 iUS − iAUS
% Fwd Premium = % interest differential
16
Covered Interest Parity (CIP)
› Thus CIP is sometimes expressed by the following
(approximate) relationship:
% Fwd Premium = % interest differential
› US-AUS interest differential = percentage forward
premium(+)/discount(-) on AUD
› if (iUS - iAUS ) > 0  forward premium on AUD
› if (iUS - iAUS ) < 0  forward discount on AUD
› The currency offering the lower nominal interest rate sells at a
forward premium; that with the higher nominal interest rate
sells at a forward discount.
17
Covered Interest Arbitrage
Foreign → domestic
Domestic → foreign
Borrowing domestic
currency
Borrowing foreign
currency
1 unit
1 unit
1 unit
Converting at
spot rate
Converting at
spot rate
1
S
SS
Loan
repayment
Investing at
foreign rate
Loan
repayment
1
(1 + i  )
S
Investing at
domestic rate
S (1 + i )
Reconverting at
forward rate
Reconverting at
forward rate
F
(1 + i )
S
1+ i
1+ i

S
(1 + i )
F
Covered margin
Covered margin
F
(1 + i ) − (1 + i )
S
S
(1 + i ) − (1 + i )
F
S, F(D/F), i* foreign i domestic
18
Outward Interest Arbitrage (Australian perspective)
S (USD / AUD)
(1 + iAUS ) 
(1 + iUS )
F(1 yr ) (USD / AUD)
› Borrow at domestic interest rate →  i Aus
› Convert borrowed funds in spot FX market at spot exchange
rate S ie sell domestic currency/buy foreign currency,
obtaining S units of foreign currency per unit of domestic
currency
→  S(USD/AUD)
› Invest in (buy) foreign currency denominated asset
→  iUS
› Sell foreign (buy domestic) currency forward
→ F(USD/AUD)
19
Inward Interest Arbitrage (Australian perspective)
S (USD / AUD)
(1 + iAUS ) 
(1 + iUS )
F(1 yr ) (USD / AUD)
› Borrow at foreign interest rate →  i US
› Convert borrowed funds in spot FX market at spot exchange
rate S ie sell foreign currency/buy domestic currency,
obtaining 1/S units of domestic currency per unit of foreign
currency
→ S(USD/AUD)
› Invest in (buy) domestic currency denominated asset
→  iAUS
› Sell domestic (buy foreign) currency forward
→ F(USD/AUD)
20
Interest Arbitrage (Australian perspective)
(iUS
 F( t ) (USD / AUD) − S (USD / AUD) 
− iAUS )  

S
(
USD
/
AUD
)


› Outward interest arbitrage (Australian perspective)
(iUS
 F(t ) (USD / AUD) − S (USD / AUD) 
− i AUS )  

S
(
USD
/
AUD
)


› Inward interest arbitrage (Australian perspective)
21
Covered Interest Parity (CIP)
› Example:
› Suppose you are given the following information:
annual interest rate on 3-month UK-pound asset, iUK= 6% pa
annual interest rate on 3-month US-dollar asset, iUS= 5% pa
spot exchange rate S(USD/pound) = USD1.50
3-month forward exchange rate F(1/4)(USD/pound) =USD1.4985
› Are there any interest arbitrage opportunities? If so determine:
› (a) in which asset you would invest
› (b) in which currency you would borrow
› (c) your interest arbitrage profit per US dollar.
22
iUK= 6% pa; iUS= 5% pa
S(USD/pound) = USD1.50 F(1/4)(USD/pound) =USD1.4985
› Step 1: Interest difference is 1%/4= 0.25%
- Pound should depreciate, however, (1.4985-1.5)/1.5*100%=-0.1%
- Pound should have depreciated more!
› Step 2:
- Borrow USD invest in Pound
- 1$/1.5($/P)*(1+6%/4)*1.4985$/P = 1.014$
› Step 3:
› Payback $: 1$*(1+5%/4)= 1.0125$
› Profit: 1.014-1.0125=0.0015$
23
Diagram of Covered Interest Arbitrage
24
Graphical Presentation of CIP
Interest Rate Differential (%)
(iUS – iAUS)
4
CIP line
2
AUD Forward
Discount (%)
-3
-1
1
3 AUD Forward
Premium (%)
-2
-4
25
Graphic Presentation of CIP (Australian perspective)
Interest Rate Differential (%)
(iUS – iAUS)
4
.B
Profitable Outward
Covered Interest
Arbitrage
CIP line
2
.A
AUD Forward
Discount (%)
-3
-1
1
-2
-4
3 AUD Forward
Premium (%)
Profitable Inward
Covered Interest
Arbitrage
26
Covered Interest Arbitrage with Bid-Offer Spreads
› Covered interest arbitrage with bid-offer exchange rates (spot and forward)
as well as bid-offer nominal interest rates (different interest rates for
borrowing & lending).
› Analysis and logic is the same!
› However you need to remember:
- price-taker in FX market buys the commodity currency at the (higher) offer
exchange rate and sells at the (lower) bid exchange rate of the market maker.
- price-taker in the money market borrows at the (higher) offer interest rate and
lends at the lower bid interest rate of the market maker.
27
Interest Rates in the External Currency Market
28
Covered Outward Arbitrage with Bid-Offer Spreads
› Borrow domestic currency at domestic offer interest rate, ia
› Convert domestic currency in spot FX market by buying foreign
currency (selling domestic currency) at spot offer rate for foreign
currency, Sa(Dom/For).
› Invest in foreign currency asset at bid foreign interest rate, i*b
› Sell foreign currency (buy domestic currency) forward at the bid
forward exchange rate for foreign currency Fb(Dom/For).
Fb ( Dom / For )
(1 + ib* ) − (1 + ia )
=
S a ( Dom / For )
29
Covered Inward Arbitrage with Bid-Offer Spreads
› Borrow foreign currency at foreign offer interest rate, i*a
› Convert borrowed foreign currency in spot FX market by buying
domestic currency (selling foreign currency) at spot bid rate for foreign
currency, Sb(Dom/For).
› Invest in domestic currency asset at bid domestic interest rate, ib
› Sell domestic currency (buy foreign currency) forward at the offer
forward exchange rate for foreign currency Fa(Dom/For).
Sb ( Dom / For )
(1 + ib ) − (1 + ia* )
=
Fa ( Dom / For )
30
Arbitrage with Bid-Offer Spreads
Foreign → domestic
Domestic → foreign
Borrowing foreign
currency
Borrowing domestic
currency
1 unit
Converting at
spot offer rate
Investing at
foreign bid rate
11unit
unit
Converting at
spot bid rate
1
Sa
Sb
Loan
repayment
Loan
repayment
1
(1 + ib )
Sa
Investing at
domestic bid rate
Sb (1 + ib )
Reconverting at
forward offer rate
Reconverting at
forward bid rate
Fb
(1 + ib )
Sa
1 + ia
Covered margin
Fb
(1 + ib ) − (1 + ia )
Sa
1 + ia
Sb
(1 + ib )
Fa
Covered margin
Sb
(1 + ib ) − (1 + ia )
Fa
S, F(D/F), i* foreign i domestic
31
Example CIA with transaction cost
› Attempting arbitrage between the US dollar and the yen at the 1-year maturity:
$10M to
invest
Bid
Ask
Spot (¥/$)
82.67
82.71
Forward (¥/$)
82.32
82.37
Dollar int. rate
0.91
1.11
Yen int. rate
0.46
0.58
› What about beginning arbitrage with borrowing yen?
- Borrow 100¥: 100¥/82.71*(1+0.91%)*82.32 = 100.434¥
- Payback: 100¥*(1+0.58%) = 100.58¥
- No profit
- Borrow $1: 1*82.67*(1+0.46%)/82.37 = $1.00826
- Payback: 1$*(1+1.11%) = $1.0111
- No profit
32
Does CIP Hold?
› Various empirical studies indicate that CIP generally
holds.
› While there are deviations from CIP, they are often
not large enough to make covered interest arbitrage
worthwhile.
› This is due to a number of factors, including:
- transaction costs,
- political risk,
- tax differentials
33
Exhibit 6.5 – Panel A
$/£ Covered Interest Arbitrage into £
34
Explaining Observed Deviations from CIP
Transaction Costs
iUS – iAUS
Zone of potential
covered outward
interest arbitrage
Zone where covered
interest arbitrage is
not feasible due to
transaction costs
CIP line
Fp
Zone of
potential
inward
covered
interest
arbitrage
35
Covered Interest Parity Deviations During the
Financial Crisis
DEV=[1+i(FC)]F/S – [1+i($)]
36
Why Deviations from Interest Rate Parity May Seem
to Exist
› Too good to be true?
- Default risks – risk that one of the counterparties may fail to honor its
contract
- Exchange controls
- Limitations
- Taxes
- Political risk
- A crisis in a country could cause its government to restrict any exchange
of the local currency for other currencies.
- Investors may also perceive a higher default risk on foreign investments.
37
The interest parity conditions I - UIP
Chapter 7.1 and 7.2
BUSINESS
SCHOOL
Speculating in the Foreign Exchange Market
Uncovered foreign money market investments
Kevin Anthony, a portfolio manager, was considering several ways to invest $10,000,000
for 1 year. The data are as follows:
USD interest rate: 8.0% p.a.; GBP interest rate: 12.0% p.a.; Spot: $1.60/£
Remember that if Kevin invests in the USD-denominated asset at 8%, after 1 year he will
have $10M * 1.08 = $10.8M
Suppose Kevin invests his $10M in the pound money market, but he decides not to hedge
the foreign exchange risk. As before, we can calculate his dollar return in three steps.
Step 1. Convert dollars into pounds in the spot market. The $10,000,000 will buy
$10M/($1.60/£) = £6.25M at the current spot exchange rate. This is Kevin’s pound
principal.
Step 2. Calculate pound-denominated interest plus principal. Kevin can invest his pound
principal at 12% yielding a return in 1 year of £6.25M * 1.12 = £7M
Step 3. Sell the pound principal plus interest at the spot exchange rate in 1 year: Dollar
proceeds in 1 year - £7M * S(t+1,$/£)
39
Uncovered Interest Rate Parity
›
40
CIP and UIP
› Covered interest rate parity: doesn’t matter where you invest –
you’ll have the same domestic currency return as long as the
foreign exchange risk is covered using a forward contract
- CIP is a covered or hedged interest parity relationship as it involves the use
of the forward FX market to cover FX risk.
› Uncovered interest rate parity – domestic and foreign
investments have same expected returns
- “uncovered” because it is maintained & restored by uncovered
interest arbitrage; arbitrage where FX risk is present!
41
CIP and UIP
› Covered Interest Parity (CIP):
F (USD / AUD)
(1 + iUS ) =
(1 + i AUS )
S (USD / AUD)
› Uncovered Interest Parity (UIP):
(1 + iUS ) =
S (E1 yr ) (USD / AUD)
S (USD / AUD)
(1 + i AUS )
where SE(USD/AUD) be the spot price of the Australian dollar expected to prevail
one year ahead
42
Uncovered Interest Parity (UIP)
› The UIP relationship is obtained by postulating that speculation
will ensure that:
› Forward exchange rate = Expected Future Spot Exchange Rate
43
Uncovered Interest Parity (UIP)
› If F(USD/AUD) < SE(USD/AUD)  speculators can buy AUD’s
forward for less than what they expect to able sell them in the
spot market in a years time  speculators go long (buy)
forward contracts →
 F(USD/AUD) .
› If F(USD/AUD) > SE(USD/AUD)  speculators can sell AUD’s
forward for more than what they expect to able buy them in the
spot market in a years time  speculators go short (sell)
forward contracts
→ F(USD/AUD).
› Such operations will stop until: F(USD/AUD) =SE(USD/AUD)
44
Uncovered Interest Parity (UIP)
› An approximate version of the UIP which is used quite
extensively links the interest differential to the expected
percentage change in the spot exchange rate.
› Specifically:
UIP:
S(E1 yr ) (USD / AUD )
S (USD / AUD )
(1 + iUS )
=
(1 + iAUS )
 S E (USD / AUD ) − S (USD / AUD ) 
 (iUS − iAUS )


S (USD / AUD )


S (USD / AUD)  (iUS − iAUS )
E
45
The Unbiasedness Hypothesis
› When the forward rate equals the expected future
spot rate, the forward rate is said to be an
unbiased predictor of the future spot rate.
› CIRP and UIRP imply the unbiased hypothesis.
46
Currency Carry Trade
› Carry Trade
- Borrow in low-yielding currencies such as the Japanese yen
or U.S. dollar and invest in higher- yielding currencies such
as the Australian dollar or the Brazilian real.
- Keep investment uncovered as to exchange rate risk.
Investment without any hedging.
- 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.
47
Currency Carry Trade Example
› Suppose the 1-year borrowing rate in USD is 1%.
› The 1-year lending rate in AUD is 4.5%.
› Borrow USD & Invest AUD without any hedging
(iAU − iUS )  S E ( AUD / USD)
› Carry (interest rate differential) = iAU –iUS= 3.5%
› The currency carry trade will be profitable if the appreciation of
USD against AUD is less than the interest rate differential (3.5%)
› Carry trade is not an arbitrage transaction, rather is a
speculation.
48
The Empirical Validity of UIP
› For UIP to be valid, the uncovered margin must fluctuate around a mean
value of zero.
› However, the empirical work show that the uncovered margins have mean
values that are significantly different from zero.
› The deviations are greater than those encountered in the case of CIP.
49
International Parity Conditions II – PPP and RIP
Chapter 8 (from 8.1 to 8.9) and 10.1
BUSINESS
SCHOOL
Where are we up to?
› Last week :
› Arbitrage activities around interest rates differences across currencies
› Interest rate parity conditions
› This week:
› Arbitrage activities around inflation differences
› Purchasing power parity
› Real exchange rate
› Real interest parity condition
› How exchange rates are determined economically
2
Purchasing Power Parity
› A simple model of the determination of exchange rates
› Baseline forecast for predicting exchange rate
› Plays a fundamental role in corporate decision making
- Location of plants
- Pricing products
- Hedging decisions
› Assessing cost of living decisions (or job opportunities?!)
3
8.1
Price Level, Price Indexes, and the
Purchasing Power of a Currency
• The general idea of purchasing power
• Nominal price – the monetary value
• Price level – the nominal price level of a country’s
“basket of goods” (consumption bundle)
• Weighted average of goods and services (i.e., we spend 1%
of our income on shoes)
• Inflation/deflation
• Inflation – when price level is rising
• Deflation – when price level is falling
• Purchasing power – inverse of price level
4
8.1
Price Level, Price Indexes, and the
Purchasing Power of a Currency
• Calculating the price level – cost of living
P (t ,$) =

N
i =1
wi P (t , i,$)
• Calculating a price index – ratio of price levels at
two different times
 P(t + k ,$) 
  100 =
PI (t + k ,$) = 
 P(t ,$) 
 w P(t + k , i,$) 100
 w P(t , i,$)
N
i =1 i
N
i =1
i
5
Exhibit 8.1 Price Indexes for the G7 Countries,
1960–2010
6
8.1
Price Level, Price Indexes, and the
Purchasing Power of a Currency
Calculating annual inflation
PI (t + 1) P(t + 1)
=
= [1 +  (t + 1)]
PI (t )
P(t )
where π(t+1) = (P(t+1) – P(t))/P(t)
From Exhibit 8.1: Italy, 1990-1991
((139.8/131.2) – 1) * 100 = 6.55%
Calculating cumulative inflation
1/ N
 PI (t + N ) 


 PI (t ) 
where t = base year
From Exhibit 8.1; U.S., 1985-2005
(179.4/100)1/20 = 1.0297 or compound annual rate of <3%
7
8.2
Absolute Purchasing Power Parity
› Internal purchasing power – the amount of goods and services that can be
purchased with $1 in the U.S.
•
If price level is $15,000, what is purchasing power of $1 mil?
•
(1/$15,000) * $1 mil = 66.67 consumption bundles
•
1/P($)
› External purchasing power - the amount of goods and services that can be
purchased with $1 outside the U.S.
- First, it is necessary to purchase some amount of pounds with the dollar
- Second, it is necessary to examine the purchasing power of those pounds in UK
•
1/S($/X) * 1/P(X)
8
8.2
Absolute Purchasing Power Parity
Absolute Purchasing Power Parity
› States that the exchange rate adjusts to equalize the internal with
external purchasing powers of a currency.
1
1
1
= PPP

P($) S ($ / X ) P( X )
› Checking the units on purchasing power calculation
•
Pounds * UK cons. bundles = UK cons. Bundles
Dollar
Pound
Dollar
› What if it doesn’t adjust? Then arbitrage is possible.
› Buy goods at cheaper price, ship them to where goods are more expensive and sell them
(of course price difference would have to be great enough to cover transportation costs)
9
8.2
Absolute Purchasing Power Parity
› Internal purchasing power of $1M based on $15,000 price level
- $1M*1/$15,000=66.67 cons. bundle
› External purchasing power of $1M based on £10,000 price level. Current
exchange rate is S($/£) = 1.4
- $1M*[1/($1.4/£)]=£714,286
- £714,286*1/ £10,000 = 71.43 cons. Bundle
› Because external PP > internal PP, one can profit from buying UK
goods and shipping them to US for resale
- Sell 71.43 cons. bundles (from UK) in US at $15,000/cons. Bundle, we
receive: $1,071,450 = (71.43*$15,000)
- $1m investment generate 7.145% return (without considering
transaction costs)
10
8.3
The Law of One Price
Overview
• The perfect market ideal
•
Big Mac should cost the same (once you convert money) no matter where
you go
• Why violations of the law of one price occur
•
Tariffs and quotas – governments often tax international shipments of goods
at their borders to protect their industries
•
Transaction costs – would you go to Italy to get a haircut?
•
Difficulty in finding buyers for some goods – while you’re looking for buyers,
either price or exchange rate may change
•
Sticky prices – sometimes there are costs for switching prices (“menu costs”)
11
8.4
Describing Deviations from PPP
› Overvalued - when its external purchasing power exceeds its internal
purchasing power
› Undervalued when its external purchasing power is less than its internal
purchasing power
› Overvaluation of one currency implies undervaluation of the other
currency in the exchange rate
- Think taller/shorter – these are relative terms
› Predictions
- Overvaluations – must weaken (depreciate)
- Undervaluations –must strengthen (appreciate)
12
8.4
Describing Deviations from PPP
Overvaluation of the dollar implies undervaluation of the pound
› Dollar (pound) price level is $15,000 (£10,000)/consumption bundle
› Exchange rate = $1.40/£
› Overvaluation of dollar relative to the pound – the external purchasing power of the dollar
> internal purchasing power
$1M * (£1/$1.40) * (1/£10,000/consumption bundle) = 71.43 consumption bundles
$1M * (1 /$15,000/consumption bundle) = 66.67 consumption bundles
› Undervaluation of the pound relative to the dollar – internal purchasing power> external
purchasing power
£1M * (1/£10,000/consumption bundle) = 100 consumption bundles
£1M * ($1.40/£1) *(1/$15,000/consumption bundle) = 93.33 consumption bundles
13
8.4
Describing Deviations from PPP
The MacPPP Standard
The Big Mac as a Price Index
- A video explanation:
- https://www.travelex.com/big-mac-index-explained
• Advantages to use:
- Standard product globally
- Local suppliers used to reduce the role of international transportation costs
- Surprisingly close to more complicated indexes
› Implied MacPPP Rates
› Overvaluations/Undervaluations
- https://www.economist.com/big-mac-index
14
Exhibit 8.2
MacPPP in
2010
15
8.5 Exchange Rates and Absolute PPPs using CPI
› How well or poorly does the theory of absolute PPP work?
› There are large and persistent deviations of actual exchange rates
from the predictions of PPP
› However, their long-term trends seem to comove
16
Exhibit 8.4 Actual USD/EUR and PPP Exchange
Rates
17
8.6
Explaining the Failure of Absolute PPP
Overview
› Changes in relative prices – what if Japanese spend more on sushi
than Americans do?
- Different weights
› Non-traded goods
- Houses
- Technology/productivity improvements
› PPP deviations and the Balance of Payments
- When a currency is overvalued (relative to that implied by the PPP), the
external purchasing power increases and consumers buy more foreign
goods, thus pulling the value of the domestic currency back down
18
Why Use PPP?
› PPP-determined exchange rates still provide a valuable
benchmark.
- One can often make more meaningful international
comparisons of economic data using PPP-determined rather
than market-determined exchange rates (for example, see
next slide).
19
8.7
Comparing Incomes Across Countries
Comparing Incomes in New York and Tokyo
$100,000 in NY versus ¥15,000,000 in Tokyo. Actual exchange rate
is ¥100/ $
•
Naï
ve Calculation: ¥15,000,000 is worth $150,000. Working in Tokyo
seems to be attractive
•
Incorporating purchasing power – you will be spending yen in Japan
not $’s. You will be indifferent if
 $100,000   15,000,000 yen 

 = 

P(t , yen) 
 P(t ,$)  
•
Working with the PPP rate – see how much NY job is worth in ¥
$100,000 * ¥160/$ = ¥16,000,000
New York job is worth more
• The PPP exchange rate provides a better estimate of the
standard of living
20
Exhibit 8.8
GDP per Capita for
OECD Countries in
2008 Using
Exchange Rates
and PPP Values
21
8.8
Relative Purchasing Power Parity
› Relative Purchasing Power Parity
•
Relative PPP states that the rate of change in the exchange rate is equal to
differences in the rates of inflation.
•
Inflation lowers the purchasing power of money
•
Exchange rates adjust in response to differences in inflation rates across
countries to leave the differences in purchasing power unchanged over time.
•
If the percentage change in the exchange rate just offsets the differential
rates of inflation, relative PPP is satisfied.
22
PPP in relative form
› If PPP holds at time points in time 0 and 1:
› t1: P1 US =S1P1AU
› t0: P0 US =S0P0AU
US
1
US
0
P
P
S 1USD / AUD P1AU
= USD / AUD AU
S0
P0
(1 + PUS ) = (1 + SUSD / AUD )(1 + P AU )
›
P
›
1 + PUS
1 + S(USD / AUD ) =
1 + P AU
PUS − P AU
S(USD / AUD ) =
1 + P AU
is the rate of change of price level
› This is also called relative form of PPP
23
8.8
Relative Purchasing Power Parity
US
UK
Price level(t)
$15,000
₤10,000
Inflation
3%
10%
Price level(t+1) $15,450
₤11,000
› Actual exchange rate St($/₤)=$1.40/₤
› According to the Absolute PPP, the pound is undervalued:
SPPPt+1($/₤)=$1.50/₤
› The pound should strengthen by 7.14% (=1.5/1.4-1).
24
8.8
Relative Purchasing Power Parity
› The absolute PPP implied exchange rate for the next year
SPPPt+1($/₤)=$1.4045/₤
› For the pound remains 7.14% undervalued
SRPPPt+1($/₤)=SPPPt+1($/₤)/1.0714=$1.3109/₤
› The pound is expected to depreciate by 6.36%.
1.3109/1.40-1=-6.36%
(3%-10%)/(1+10%) = -6.36%
25
Relative form of PPP
› Using  represents the rate of price changes (inflation), by approximation:
1 + S (USD / AUD) =
› or
1 +  USD
1 +  AUS
S (USD / AUD) =  US −  AU
› Actual % appreciation in exchange rate = US-AUS inflation differential
› Relative PPP stipulates that:
If US > AUS  S(USD/AUD) > 0 ie appreciation of AUD
If US < AUS  S(USD/AUD) < 0 ie depreciation of AUD
26
8.9 The Real Exchange Rate
› The definition of the real exchange rate – the exchange rate adjusted
for inflation
RS (t ,$ / euro ) =
S (t ,$ / euro )  P(t , euro )
P(t ,$)
› Real appreciations and real depreciations – changes in forex rate
adjusted for inflation
•
An increase in the nominal forex rate ($/€), holding $ prices and € prices
constant
•
An increase in the € prices of goods holding the $ prices of goods
constant
•
An increase in the $ prices of goods holding the € prices of goods
constant
27
8.9 The Real Exchange Rate
›
28
8.9 The Real Exchange Rate
US
UK
Price level(t)
$15,000
₤11,000
Inflation
4%
8%
Price level(t+1) $15,600
₤11,880
› St($/₤)=$1.30/₤
› RSt($/₤)=$1.30/₤*(₤11,000/$15,000)=0.9533.
› SRPPPt+1($/₤)=$1.30/₤*(1.04/1.08)=$1.2519/₤
› RSt+1($/₤)=$1.2519/₤*(₤11,000*1.08/$15,000*1.04)
= 0.9533.
29
Real Interest Parity (Fisher-Open Condition)
› The Real Interest Parity(RIP) condition stipulates that
real interest rates should be equal across countries and
currencies. This condition is also sometimes referred to
as the Fisher-open condition.
› The famous American economist Irving Fisher defined
the real interest as being equal to the nominal interest
minus the expected rate of inflation.
› The Australian real interest rate: rAUS = iAUS - EAUS
› The US real interest rate: rUS = iUS - EUS
› Real Interest Parity (RIP):
(iUS - EUS) = (iAUS - EAUS )
rUS = rAUS
30
10.1 Parity Conditions and Exchange
Rate Forecasts
› The International Parity Conditions
• CIRP – Covered Interest Rate Parity
- Links forward rates, spot rates, and interest rate differentials
• UIRP or Unbiasedness – Uncovered Interest Rate Parity
- Sometimes called International Fisher Effect/Relationship
- Links expected exchange rate changes and interest rate differentials
• PPP
- Links inflation rates and rates of changes in forex rates
31
Real Interest Parity
› RIP can be derived by combining UIP and
expectation form of PPP.
S F / D e = i F − i D
S F / D
e
= F
e
−D
e
 F e −  De = i F − i D
i F −  F e = i D −  De
r =r
F
› Thus:
D
› This shows that real interest rates must be equal
across countries
32
The interrelationship of the parity
conditions
UIP :
PPP(exp.):
RIP:
iF − iD = S F / D e
 F e −  D e = S F / D e
iD −  D e = iF −  F e
› UIP, PPP(exp.), and RIP conditions are related. Any one of
the above conditions can be derived from the other two.
› If UIP and PPP (exp.) hold precisely, then RIP also holds
› If RIP and UIP hold, then PPP (exp.) also holds
› If RIP and PPP (exp.) hold precisely, then UIP also holds
33
How RIP, UIP and PPP are related
Parities:
iF - iD
RIP
UIP
SSe
 F e −  De
e
F/D
PPP(exp)
34
Exhibit 10.2
An Example of
International Parity
Conditions: The United
Kingdom and
Switzerland
35
Testing the PPP Theory
Conceptual Test
› Plot the actual inflation differential and exchange rate % change for two or
more countries on a graph.
› If the points deviate significantly from the PPP line over time, then PPP
does not hold.
36
Tests of PPP based on annual data from 1982 to 2004
37
Testing the PPP Theory
Statistical Test
› Apply regression analysis to the historical exchange rates and inflation
differentials
:
› SF/D = a0 + a1 [(1+F)/(1+D) - 1]+ m
› The appropriate t-tests are then applied to a0 and a1, whose
hypothesized values are 0 and 1 respectively.
38
The Empirical Validity of PPP
› There is little empirical evidence to support the
validity of PPP, particularly in the short run.
› There is some evidence for PPP under
hyperinflation and over long periods of time.
› However, the use of inflation differentials to
forecast long-run movements in exchange rates
is supported.
39
What have we learned?
› Parity conditions are introduced, which include the CIP,
PPP, and RIP.
› These parity conditions are developed in the context of the
perfect capital market assumptions.
› These conditions can be thought of as international
financial “benchmarks” or “break-even values”.
› The parity conditions heavily rely on arbitrage, a violation of
parity often implies a direct or indirect profit opportunity.
40
Foreign Currency Derivatives I
Futures and Options
Chapter 20.1, 20.2, 20.3, and 20.4
BUSINESS
SCHOOL
20.1 The Basics of Futures Contracts
› A futures contract is like a forward contract in that it
specifies that a certain currency will be exchanged for
another at a specified time in the future at prices
specified today.
› A futures contract is different from a forward contract in that
futures are standardized contracts trading on organized
exchanges with daily resettlement through a
clearinghouse.
2
Futures contract specifications
›Example:
A contract to trade AUD100,000 (for US
dollars) for December 2021 at the exchange
rate of 0.7500 USD per AUD.
1.Size – notional principle
2.Price–spot rate “American terms”
3.Delivery date
4.Trading can last till the second business
day prior to the maturity
3
20.1 The Basics of Futures Contracts
› Standardizing features for futures contracts:
- Contract size: Standardized, smaller amounts (e.g., ¥12.5M, €125,000,
C$100,000)
- Delivery month: Fixed maturities (e.g., 30, 60, 90, 180, 360 days)
- Daily resettlement
› On the other hand, in forward contracts:
- dates, quantities, and other aspects of the contract are determined by
private negotiation between the two parties.
4
Payoff Profiles – 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.
Long
position
S180(USD/AUD)
0
F180(USD/AUD)= 0.8
loss
If you agree to buy anything in the future
at a set price and the spot price later falls
then you lose.
5
Payoff Profiles – Short Position
profit
If you agree to sell anything in the future
at a set price and the spot price later falls
then you gain.
S180(USD/AUD)
0
F180(USD/AUD)= 0.8
loss
If you agree to sell anything in the
future at a set price and the spot price
later rises then you lose.
Short
position
6
20.1 The Basics of Futures Contracts
• Margins
›
Credit risk is handled by setting up an account called a margin
account, wherein they deposit an asset to act as collateral
•
The first asset is called the initial margin
•
Depend on size of contract and variability of currency involved
›
Marking to market – deposit of daily losses/profits
›
Maintenance margins – minimum amount that must be kept in
the account to guard against severe fluctuations in the futures
prices (for CME, about $1,500 for USD/GBP and $4,500 for
JPY/USD)
• Margin call – when the value of the margin account reaches the
maintenance margin
›
the account must be brought back up to its initial value
7
Futures Terminology
› Exchange Clearing House
- Middleman in a futures contract transaction;
- Places itself between buyers (long) and sellers (short) of futures
contracts on organized exchanges;
- Guarantees that every futures contract will be fulfilled even if one of the
parties defaults.
8
Futures Terminology
› 'Closing Out' of a Position
- method used to end the obligation underlying an existing futures contract; go
long if you have a short position in a futures; go short if you have a long
position in a futures.
- E.g An investor who has purchased two June 2021 Australian dollar futures
contracts (gone long 2 contracts) can unwind or close-out their obligations by
selling two June 2021 Australian dollar contracts ( go short 2 contracts) before
June 2021. Clearinghouse recognises this and accordingly cancels out the
two positions.
9
Daily Marking-to-Market & Settlement
› Marking-to-market  market participants realise their
profit or suffer their losses on their futures contract
positions, on a day-to-day basis.
› Depending on how futures prices move from one day to
the next, customers’ margin accounts are either credited
or debited.
- decreased, if futures prices move such that the position would
show a loss if liquidated
- increased, if futures prices move such that the position would
record a profit if liquidated.
10
Daily Marking-to-Market & Settlement
› Margining requirements that are in place on
organised exchanges thus ensure that every open
futures contract:
- is always covered by a minimum deposit (maintenance margin)
- all profits and losses are received and paid as soon as they occur.
› Margining requirements and daily marking-to-market
provisions thus effectively minimise the chance of
default on a futures contract.
11
Daily Resettlement: An Example
› Consider a long position in the CME US/Euro contract
(You are buying Euro in the future).
› It is written on €125,000 and quoted in $ per €.
› The strike price is $1.30 per € the maturity is 3 months.
› At initiation of the contract, the long posts an initial margin
of $6,500.
› The maintenance margin is $4,000.
12
Performance Bond Money
› Each day’s losses are subtracted from the investor’s
account.
› Each day’s gains are added to the account.
› In this example, at initiation the long posts an initial margin
of $6,500.
› The maintenance margin is $4,000.
- If this investor loses more than $2,500, he has a decision to make;
he can maintain his long position only by adding more funds, and if
he fails to do so his position will be closed out with an offsetting short
position.
13
Daily Resettlement: An Example
› Over the first 3 days, the euro strengthens then depreciates in
dollar terms:
Settle
Gain/Loss
Account Balance
$1.31
$1,250 = ($1.31 –$7,750
$6,500 + $1,250
$1.30)×=125,000
$1.30
–$1,250
$6,500
$1.27
–$3,750
$2,750 + $3,750 = $6,500
On day three suppose our investor keeps his long
position open by posting an additional $3,750.
14
Daily Resettlement: An Example
› Over the next 2 days, the long keeps losing money and closes
out his position at the end of day five.
Settle
$1.31
$1.30
$1.27
$1.26
$1.24
Gain/Loss
$1,250
–$1,250
–$3,750
–$1,250
–$2,500
Account Balance
$7,750
$6,500
$2,750 + $3,750 = $6,500
$5,250 = $6,500 – $1,250
$2,750
15
Prices and the Margin Account
$/€ Futures Price
Margin
Account
Initial
Margin
Maintenance
Margin
Margin Calls
Time
16
20.1 The Basics of Futures Contracts
› The adjustments made to this investor’s long June
futures position are mirrored by similar (but oppositely
signed) adjustments to an investor that has taken out
a short position in the same futures contract (ie has
sold a June British pound futures contract).
› When buyer’s margin account is adjusted up, seller’s
margin account is adjusted down by the same
amount. What buyers gain, sellers lose.
› Futures trading is a zero sum game.
17
Reading a Table of Futures Quotes
Open
Hi
Lo
Settle Change Lifetime
High
Sept .9282 .9325 .9276 .9309 +.0027
1.2085
Lifetime
Low
Open
Interest
.8636
74,639
Highest and lowest
Daily Change prices over the
Closing price
lifetime of the
Lowest price that day
contract.
Highest price that day
Opening price
Number of open contracts
Expiry month
18
Forward Contracts vs Futures Contracts
FORWARDS
FUTURES
Private contract between 2 parties
Non-standard contract
Settled at maturity
Delivery or final cash
settlement usually occurs
Subject to credit risk
No explicit collateral
Exchange traded
Standard contract
Settled daily
Contract usually closed out
prior to maturity
No credit risk
Initial margin and marked to market
19
Using Currency Futures for Speculation
› Speculators often sell currency futures when they expect the
underlying currency to depreciate, and vice versa.
April 4
June 17
1. Contract to sell
500,000 pesos
@ $.09/peso
($45,000) on
June 17.
2. Buy 500,000 pesos
@ $.08/peso
($40,000) from the
spot market.
3. Sell the pesos to
fulfill contract.
Gain $5,000.
20
Using Currency Futures for Hedging
› Currency futures may be purchased by MNCs to hedge foreign
currency payables or sold to hedge receivables.
April 4
June 17
1. Expect to receive
500,000 pesos.
Contract to sell
500,000 pesos
@ $.09/peso on
June 17.
2. Receive 500,000
pesos as expected.
3. Sell the pesos at
the locked-in rate.
21
Closing out Currency Futures Position
› Holders of futures contracts can close out their positions by selling
similar futures contracts. Sellers may also close out their positions
by purchasing similar contracts.
January 10
1. Contract to
buy
A$100,000
@ $.53/A$
($53,000) on
March 19.
February 15
2. Contract to
sell
A$100,000
@ $.50/A$
($50,000) on
March 19.
March 19
3. Incurs $3000
loss from
offsetting
positions in
futures
contracts.
22
20.2 Hedging Transaction Risk with Futures
It is mid-February and Nancy Foods (US company) expects a receivable of
€250,000 in one month
- Will need 2 contracts (since they are €125,000)
- Wants to receive $’s when the € weakens (protect against a loss in receivable) –
SELL A € CONTRACT
- If contract delivery date coincides with receivable date, maturity is matched perfectly
- Example: February: Spot ($1.24/€); Future ($1.23/€); March: Spot ($1.35/€); Future
($1.35/€); 30-day i€=3% p.a.; receivable in 30 days
Value upon receipt of money (mid-March)
- Sell receivable in spot market in March = $250,000 * $1.35/€ = $337,500
- Loss on futures contract: [($1.23/€)-($1.35/€)]*€250,000=-$30,000
- Combination of CFs: $337,500 - $30,000=$307,500
- Effective exchange rate: $307,500/€250,000=$1.23/€, but
this is the futures rate, so it shows that they are hedged
23
Basics of Options Contracts
› 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.
› Calls vs. Puts:
- Call options give the holder the right, but not the obligation,
to buy a given quantity of some asset at some time in the
future at prices agreed upon today.
- Put options give the holder the right, but not the obligation,
to sell a given quantity of some asset at some time in the
future at prices agreed upon today.
24
Basics of Options Contracts
call
put
Buyer (holder)-long
position
Pays a premium
Right to buy
Right to sell
Seller(writer)-short
position
Receives a premium
Obligation to sell
(if the option is
exercised)
Obligation to buy
(if the option is
exercised)
25
Basics of Options Contracts
› European versus American options:
- European options can only be exercised on the expiration date
while American options can be exercised at any time up to and
including the expiration date.
- American options are usually worth more than European
options, other things equal.
› Moneyness
- If immediate exercise is profitable, an option is “in the money.”
- Out of the money options can still have value.
26
Option Terminology
› Exchange-Traded Options
› Standardised option contracts that trade organised
exchanges in accordance with rules & regulations
stipulated by the exchange.
› Over-The-Counter Options (OTC)
› Option contracts whose terms and conditions are
tailored to the specific needs of the two parties
involved
27
Option Terminology
› Exercise of Option
› The process of enforcing the right that has been
purchased; the act of buying or selling the underlying
currency in accordance with the terms in the option
contract.
› Action which can only be taken by the buyer or holder
of option contract.
› Exercise or Strike Exchange rate
› The predetermined exchange rate in the option
contract at which option buyer/holder can buy or sell
the underlying currency should they choose to
exercise the option contract.
28
Option Terminology
› Option Premium
› The sum of money paid by the option buyer to the option
seller in order to obtain the option contract. Arrived at by
negotiation between option buyers and sellers.
› Kept by seller whether or not option contract is
“exercised” by option buyer.
› Option Expiration Date
› The date after which the option contract cannot be
exercised. (The date after which the option holder’s right
to buy or sell the currency will no longer be valid).
29
PHLX Currency Option Specifications
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
30
The premium is quoted in US cents, that is, for each SF traded the
price of option is 0.5 US cents.
The total cost of one call option contract is
SF62,500 ×$0.0050/SF=$312.50
31
Determinants of Option Premiums
› The value or price of an option (option premium) consists of 2 basic
components:
› Intrinsic Value
› Time Value
Option
Premium
=
Intrinsic
Value
+
Time
Value
32
Intrinsic Value
› Relationship between current market price of underlying asset
and exercise price of the option ie the "money-ness" of the option.
› The profit that could be made if option was exercised immediately.
› Greater the intrinsic value of option, the higher would be the value
of the option, and hence the greater the option premium.
33
Time Value
› What investors are prepared to pay for the potential to
profit in the future from favorable exchange rate
movements.
› The greater the time value, the greater is the chance to
exercise the option at a profit, and the hence the more
valuable is the option.
34
Intrinsic Value & Time Value for an American Call Option
Profit
The red line shows
the payoff at
maturity, not profit,
of a call option.
Long 1 call
Intrinsic value
Note that even an
out-of-the-money
option has value—
time value.
Time value
Out-of-the-money
loss
ST
In-the-money
E
35
Factors Affecting Currency Option Values
.
Exchange rate of the
underlying currency
Exercise exchange rate
Exchange rate volatility
Interest rate on the
currency of purchase
Expected appreciation of
underlying currency
(Forward premium/discount
or interest differential)
Time to expiry
Call Option
Put Option
+
_
+
+
_
+
+
_
+
_
+
+
36
20.3 Basics of Foreign Currency Option Contracts
Example: A Euro Call Option Against Dollars
A particular euro call option offers the buyer the right (but not the
obligation) to purchase €1M @ $1.20/€.
If the price of the € > exercise rate($1.20/€), owner will exercise
To exercise: the buyer pays ($1.20/€)* €1M=$1.2M to the seller and the
seller delivers the €1M
The buyer can then turn around and sell the € on the spot market at a
higher price!
For example, if the spot is, let’s say, $1.25/€, the revenue is:
[($1.25/€)-($1.20/€)]* €1M = $50,000 (payoff, NOT the profit)
37
20.3 Basics of Foreign Currency Option Contracts
Example: A Yen Put Option Against the Pound
A particular yen put option offers the buyer the right (but not the
obligation) to sell ¥100M @ £0.6494/¥100.
If the price of the ¥ <exercise rate, owner will exercise (think insurance)
To exercise: the buyer delivers ¥100M to the seller
The seller must pay (£0.6494/¥100)* ¥100M = £649,400
For example, let’s say the spot at exercise is £0.6000/¥100.
The revenue then is:
[(£0.6494/¥100)-(£0.6000/¥100)]* ¥100M = £49,400 (payoff, NOT the
profit)
38
Payoffs and Profits on Options at
Expiration - Calls
Notation
Terminal exchange rate = ST
Exercise Price = X
Payoff to Call Holder
Payoff to Call Writer
(ST - X)
if ST >X
- (ST - X)
if ST >X
0
if ST < X
0
if ST < X
Profit to Call Holder
Payoff – Option Premium
Profit to Call Writer
Payoff + Option Premium
39
Payoffs and Profits at
Expiration - Puts
Payoffs to Put Holder
Payoffs to Put Writer
0
if ST > X
0
if ST > X
(X - ST)
if ST < X
-(X - ST)
if ST < X
Profit to Put Holder
Payoff – Option Premium
Profits to Put Writer
Payoff + Option Premium
40
Long Currency Call on Euro
Profit from buying a Euro European call option: option price = 5 US
cents, strike Ex-rate = 100 US cents/Euro
30 Profit (US cents)
20
10
70
0
-5
80
90
100
Terminal
Exchange rate (US$/Euro)
110 120 130
41
Short Currency Call on Euro
Profit from writing a Euro European call option: option price = 5 US
cents, strike Ex-rate = 100 US cents/euro
Profit (US cents)
5
0
-10
110 120 130
70
80
90 100
Terminal
Exchange rate (US$/euro)
-20
-30
42
Long Currency Put on AUD
Profit from buying an AUD Currency European put option:
option price = 7c, strike price = 70c
30 Profit (cents)
20
10
0
-7
Terminal
Exchange rate (USD/AUD
40
50
60
70
80
90 100
43
Short Currency Put on AUD
Profit from writing an AUD Currency European put option:
option price = 7 US cents, strike price = 70 US cents
Profit (cents)
7
0
40
50
Terminal
Exchange rate (USD/AUD
60
70
80
90 100
-10
-20
-30
44
20.4 The Use of Options in Risk Management
A bidding situation at Bagwell Construction – U.S. company wants to bid
on a building in Tokyo (in yen)
›
Double sources of risks:
›
•
1) future exchange rate (need to convert (sell) JPY to USD)
•
2) may or may not get the project
Can’t use forward hedge. Why?
•
If the company doesn’t get the contract, it must still sell the JPY from a
forward contract
› Option allows flexibility in case they don’t win!
›
Which option should be used?
•
Buy a put option on JPY (against USD): the right to sell JPY at fixed rate
•
What if the company doesn’t get the contract?
•
The maximum loss is the premium of a put option
45
20.4 The Use of Options in Risk Management
It is Friday, 10/1/10: Pfimerc has a receivable of £500,000 on Friday, 3/19/11.
Spot (U.S. cents per £): 158.34
170-day forward rate (U.S. cents per £): 158.05
U.S. dollar 170-day interest rate: 0.20% p.a.
British pound 34-day interest rate: 0.40% p.a.
Option data for March contracts in $/£:
Strike
158
159
160
Call Prices
5
4.52
4.08
Put Prices
0.0481
0.0533
0.0589
How should Pfimerc hedge?
£ Put Option: gives them the right (but not the obligation) to sell pounds
at a specific price if the £'s value falls
Because Pfimerc wants to sell £500,000, it must pay:
£500,000 * ($0.0481/£) = $24,050
They will exercise if the £ falls below $1.58/£
500,000 * $1.58/£ = $790,000 if S(t+170) ≤ $1.58/£
They will sell £'s in the spot market if the £ is worth more than $1.58
500,000 * S(t+170) > $790,000 if S(t+170) > $1.58/£
Either way, the cost of the put in 170-day (not now) = [$24,050*(1+(0.002*170/360))]=$24,073
The minimum revenue is therefore: $790,000-$24,073=$765,927
46
Exhibit 20.5 Hedging Pound Revenues
47
20.4 The Use of Options in Risk Management
When you will sell an asset in the future and want to lock in the price,
short hedge is appropriate: short forward or buy a put option
- Previous example for Pfimerc: an exporter of products from US to UK
When you will purchase an asset in the future and want to lock in the
price, long hedge is appropriate: long forward or buy a call option
- The case of an importer who must pay in the exporter’s currency
- Importing watches to the US from Switzerland (Example 8 from textbook)
48
Lecture:
Foreign Currency Derivatives II: Swaps
Chapter 21
BUSINESS
SCHOOL
Definitions
› In a swap, two counterparties agree to a contractual
arrangement wherein they will exchange cash flows at periodic
intervals.
› There are two types of interest rate swaps.
- Single currency interest rate swap
- “Plain vanilla” fixed-for-floating swaps are often just called
interest rate swaps.
- Cross-currency interest rate swap
- This is often called a currency swap; fixed for fixed rate debt
service in two (or more) currencies.
Interest Rate Swap Diagram
An Example of a “Plain Vanilla” Interest Rate Swap
–An agreement by Microsoft with Intel to receive 6-month LIBOR + 1% &
pay a fixed rate of 8.25% per annum every 6 months for 3 years on a
notional principal of $100 million
Pay 8.25%
Intel
Microsoft
LIBOR + 1%
–LIBOR (London InterBank Offered Rate): floating interest rate
–the amount of interest rate is determined at the beginning of the period,
and is paid at the end of the period
Cash Flows to Microsoft
---------Millions of Dollars--------LIBOR FLOATING
FIXED
Net
Date
Rate
Cash Flow Cash Flow Cash Flow
Mar.5, 2007
8.2%
Sept. 5, 2007
8.8%
+4.10
–4.125
–0.025
Mar.5, 2008
7.3%
+4.40
–4.125
+0.275
Sept. 5, 2008
7.5%
+3.65
–4.125
-0.475
Mar.5, 2009
7.6%
+3.75
–4.125
-0.375
Sept. 5, 2009
7.9%
+3.80
–4.125
-0.325
Mar.5, 2010
8.4%
+3.95
–4.125
-0.175
• In an interest rate swap, two companies do NOT exchange notional
principal, since exchanging $100M will have no financial value.
An Example of a “Plain Vanilla” Interest Rate Swap
– The net borrowing costs are:
Microsoft: (LIBOR + 1.5%) + 8.25% - (LIBOR + 1%) = 8.75% p.a. net
Intel:
8% + (LIBOR + 1%) – 8.25% = LIBOR + 0.75% p.a. net
Pay 8.25%
Intel
Microsoft
LIBOR + 1%
Borrow at fixed
rate and pay 8%
p.a. (e.g., issue a
corporate bond)
Borrow at variable
rate and pay LIBOR
+ 1.5% (e.g., borrow
money from a bank)
Situation of Microsoft under Swap
› Microsoft transforms original floating-rate loan into fixed
rate loan.
› With swap it has 3 sets of cash flows:
- 1. Pays LIBOR + 1.5% to outside lenders
- 2. Receives LIBOR + 1% from Intel under the terms of the
swap
- 3. Pays 8.25% to Intel under the terms of the swap
› These cashflows net out to:
(LIBOR + 1.5%) + 8.25% - (LIBOR + 1%) = 8.75% p.a.
- swap transforms floating-rate loan at LIBOR + 1.5%
into fixed-rate loan at 8.75%
Situation of Intel under Swap
› Intel transforms original fixed-rate loan into floating-rate
loan.
› Cash flows under swap:
› 1. Pays 8% to outside lenders
› 2. Pays LIBOR + 1% to Microsoft under the terms of
the swap
› 3. Receives 8.25% from Microsoft under the terms of
the swap
› These cashflows net out to:
8% + (LIBOR + 1%) – 8.25% = LIBOR + 0.75%
› swap transforms fixed-rate loan at 8% into floating-rate
loan at LIBOR + 0.75%
Situation of Microsoft under Swap
(with financial intermediary)
Intel
8.15%
L+1.05%
Financial
Intermediary
8.2%
L+0.9%
Microsoft
• Financial intermediary:
Net cash flows : - (8.15%) + (LIBOR + 1.05%) + (8.2%) –
(LIBOR+0.9%) = 0.2% or 20 bp
• On notional principal of $100m financial institution earns $200,000
p.a for 3 year period over the life of swap.
• $200,000 is a compensation for risk that one of the two companies
default. If one of the companies defaults, the financial intermediary
sill has to honor its agreement
Comparative Advantage
Comparative advantage argument: commonly used
explanation for why swap is so popular
› AAACorp wants to borrow floating
› BBBCorp wants to borrow fixed
Fixed
Floating
AAACorp
10.00%* 6-month LIBOR + 0.30%
BBBCorp
11.20%
6-month LIBOR + 1.00%*
› Absolute advantage: AAA can borrow at lower costs in both fixed
and floating markets, since AAA has higher credit rating
Comparative Advantage
AAACorp
BBBCorp
Fixed
Floating
10.00%* 6M LIBOR + 0.30%
11.20% 6M LIBOR + 1.00%*
Difference in fixed rate market
= ( 11.2% - 10.0%) = 1.2%
Difference in floating rate market
= [(Libor + 1.0%) - (LIBOR + 0.30%) = 0.7%
› Difference in fixed rate market is comparatively greater!
› AAA has a comparative advantage in fixed rate market.
- AAA has more advantage in fixed rate market
› BBB has a comparative advantage in floating rate market.
- BBB has less disadvantage in floating rate market
Comparative Advantage
› Net difference in quality spreads
= (1.2% - 0.7% ) = 0.5%
› This represents the potential gains to be made by the two
counterparties collectively via entering into a swap.
- AAA should follow its comparative advantage & borrow in
fixed rate market.
- BBB should follow its comparative advantage & borrow in the
floating rate market.
- They should then swap their respective interest payments.
Comparative Advantage
AAACorp
BBBCorp
Fixed
Floating
10.00%* 6M LIBOR + 0.30%
11.20% 6M LIBOR + 1.00%*
9.95%
Borrow at 10%
from fixed rate market
AAA
BBB
Borrow at LIBOR+1%
from floating rate market
LIBOR
•AAA: - (10%) + (9.95%) - (LIBOR) = - ( LIBOR + 0.05%) compare to 6-month
LIBOR + 0.30%
•BBB: - (LIBOR+1%) + (LIBOR) - (9.95%) = - 10.95% compare to 11.20%
Situation of AAA Corp under Swap
› AAA’s cashflows under swap :
› 1. Pays 10% p.a to outside lenders
› 2. Receives 9.95% p.a from BBB under the terms of the
swap
› 3. Pays LIBOR to BBB under the terms of the swap
› These cashflows net out to: - (10%) + (9.95%) - (LIBOR)
= - ( LIBOR + 0.05%)
› For AAA swap transforms fixed-rate loan into a floatingrate loan at LIBOR + 0.05%.
› This 0.25% p.a lower than what AAA would pay if it went
to floating rate market directly
Situation of BBB Corp under Swap
› BBB’s cash flows under swap :
› 1. Pays LIBOR + 1% p.a to outside lenders
› 2. Receives LIBOR from AAA under the terms of the swap
› 3. Pays 9.95% p.a to AAA under the terms of the swap
› These cash flows net out to: - (LIBOR+1%) + (LIBOR) (9.95%) = - 10.95%
› For BBB swap transforms floating-rate loan into a fixed-rate
loan at 10.95%.
› This 0.25% p.a lower than what BBB would pay if it went to
fixed rate market directly!
› Total Swap gain = 0.25% for A + 0.25% for B
= 0.5% = Net difference in quality spreads =(1.2%-0.7%)
Swap with financial intermediary
9.93%
9.97%
10%
AAA
F.I
.
LIBOR
BBB
LIBOR+1%
LIBOR
After swap:
BBB: -10.97% compared with -11.2% save 0.23%
AAA: -(LIBOR+0.07%) compared with -(LIBOR+0.3%) save 0.23%
F.I. profit 0.04%
Total swap gain: 0.46%+0.04% = 0.5%
Currency Swaps
› An agreement between two parties to exchange the CFs of
two long-term bonds denominated in different currencies
- Parties exchange initial principal amounts (at spot)
- Parties pay interest on the currency they initially receive, receive
interest on the currency they initially pay and reverse the exchange of
initial principal amounts at a fixed future date
- Basic currency swap involves exchange of fixed-for fixed-rate
- One of the most common reasons of using currency swaps is that you
need money in a currency A but you borrow money in another
currency B (to convert to A); you’re concerned about future foreign
exchange fluctuations.
Foreign Currency Swap Diagram
An Example of a Currency Swap
An agreement to pay 5% per annum on a sterling
principal of £10,000,000 & receive 6% per annum on a
US$ principal of $18,000,000 every year for 5 years
Exchange of Principal
› In an interest rate swap the principal is not exchanged
› In a currency swap the principal is usually exchanged at
the beginning and the end of the swap’s life
The Cash Flows
Dollars
Pounds
$
Years
0
£
------millions-----–18.00
+10.00
1
+1.08
–0.5
2
+1.08
–0.5
3
+1.08
–0.5
4
+1.08
–0.5
5
+19.08
-10.5
Comparative Advantage Arguments for Currency Swaps
Without swap:
General Motors wants to borrow AUD
Qantas wants to borrow USD
USD
AUD
General Motors 5.0%
12.6%
Qantas
13.0%
7.0%
21
Currency Swap
› Differential in US market = (7% - 5%) = 2% p.a
› Differential in AUS market = (13.0% - 12.6%) = 0.4%
p.a
› Total gain to both parties in swap = 1.6% p.a
› GM has a comparative advantage in raising USD loans
› QANTAS has comparative advantage in raising AUD
loans
With swap:
General Motors can transform USD loan to AUD loan.
Qantas wants can transform AUD loan to USD loan.
Currency Swap
USD
General Motors 5.0%
Qantas
7.0%
USD 5.0%
AUD
12.6%
13.0%
USD 6.3%
USD 5%
GM
F.I.
Qantas
AUD 13%
AUD 11.9%
AUD 13.0%
•Qantas: net interest payments = -13.0% - 6.3% + 13.0% = -6.3% p.a
(USD) compare to 7%
•GM: net interest payments = -5.0 - 11.9 + 5.0 = -11.9% p.a (AUD)
Compare to 12.6%
•Fi: gains 1.3%p.a on USD cashflows and losses 1.1% on AUD cashflows
net gain to FI = 0.2% p.a
Currency Swaps Quotation
› Financial intermediaries typically quote bid-offer rates for fixed foreign
currency interest rates at which they were willing to swap versus paying or
receiving floating interest rate payments.
› For example:
- USD: 7% bid and 7.2% offered against 6-month dollar LIBOR
- EURO : 5% bid and 5.2% offered against 6-month dollar LIBOR
› The bank is willing to:
- Pay fixed interest rate of 7% in USD or 5% in Euro, against receiving 6 month
dollar LIBOR.
- Pay 6-month LIBOR, against receiving fixed interest rate of 7.2% in USD or 5.2%
in Euro.
Currency Swaps Quotation
Interpretation:
Euro-€
Bid
3 year
5.00
Ask
5.20
U.S. $
Bid
Ask
7.00
7.20
› Swap bank pays €5% for LIBOR and receives $7.2% for
LIBOR ⇒ It pays €5% for $7.2%.
› Swap bank pays $7% for LIBOR and receives €5.2% for
LIBOR ⇒ It pays $7% for €5.2%.
25
Currency Swaps Quotation
› Swap bank pays €5% for LIBOR and receives $7.2% for
LIBOR ⇒ It pays €5% for $7.2%.
› Swap bank pays $7% for LIBOR and receives €5.2% for
LIBOR ⇒ It pays $7% for €5.2%.
Firm $7.0%
A
€5.2%
Swap
Bank
Firm
B
€5.0%
$7.2%
26
Currency swaps illustration
› Consider Firms A and B:
- Firm A (U.S. MNC) wants to borrow €40 million for 3 years for its French
subsidiary.
- Firm B (French MNC) wants to borrow $60 million for 3 years for its U.S.
subsidiary.
$
€
A
$7%
€6%
B
$8%
€5%
› The current exchange rate is $1.50 = €1.00.
› Suppose both subsidiaries will generate enough cash flows to
service their debt.
27
Foreign Exchange Risk
› What if U.S. MNC borrows in its national capital market ($)?
- Borrows $60m, convert to €40, and invest.
- French sub. will generate cash flows to pay interests and principal.
- Then it creates transaction exposure: What if dollar appreciates
against Euro in the future?
› What if U.S. MNC borrows in Euro?
- It may have to borrow at a unfavorable interest rate because it may
not be not well-known.
› The French MNC also faces a similar (symmetric) problem.
28
Currency swaps illustration
› Suppose a swap bank recognizes the financing needs of the
two MNCs and quotes the following:
Euro-€
Bid
3 year
5.00
U.S. $
Ask
5.20
Firm $7.0%
A
€5.2%
Swap
Bank
Bid
Ask
7.00
7.20
Firm
B
€5.0%
$7.2%
29
Currency swaps illustration
› Suppose that Firm A borrows $60m locally at $7% and then
trades $60m for €40m at spot.
$60m
Bank
X
$7.0%
$60m
Firm
A
$7.0%
€5.2%
€40m
Swap
Bank
$
€
A
$7%
€6%
B
$8%
€5%
30
Currency swaps illustration
› Suppose that Firm B borrows €40m locally at €5%, then
trades €40m for $60m.
$60m
Swap
Bank
Firm
B
€5.0%
$7.2%
€40m
€5%
€40m
Bank
Y
$
€
A
$7%
€6%
B
$8%
€5%
31
Currency swaps illustration
Swap bank earns 40bp per year (20bp in $ and 20bp in €).
Firm
A
$7.0%
€5.2%
Swap
Bank
Firm
B
€5.0%
$7.2%
The notional size is $60m.
The tenure is for 3 years.
Firm A earns 80bp per year on the swap and
hedges exchange rate risk.
Bank
X
Firm B earns 80bp per year on the swap and
hedges exchange rate risk.
Bank
Y
32
Valuation of an Existing Swap
› When the contract is initiated, swaps have zero
value.
› Any swap’s value is the difference in the present
values of the payment streams that are incoming and
outgoing.
- Plain vanilla fixed for floating swaps get valued just like a
pair of bonds.
- Currency swaps get valued just like two bonds denominated
in two different currencies.
33
Swap Valuation Example
› A currency swap has a remaining life of 18 months.
› It involves exchanging interest at 14% on £20 million
for interest at 10% on $30 million once a year.
• The term structure of interest rates is currently flat
in both the U.S. and the U.K.
› If the swap were negotiated today, the interest rates
exchanged would be $8% and £11%.
• All rates were quoted with annual compounding.
› The current exchange rate is $1.65 = £1.
› What is the value of the swap (in USD) to the party
paying dollars and receiving pounds?
34
Swap Valuation Example
18
6
£2.8m
£22.8m
–$33m
–$3m
Value of the swap to the party paying dollars:
0
£2.8m
£22.8m
$1.65
$36,553,870 = (1.11)1/2 + (1.11)3/2 × £1
–$32,288,848 = –$3m 1/2 + –$33m3/2
(1.08)
(1.08)
$4,265,002
35
Review Question: Develop a Swap Contract
Alpha and Beta Companies can borrow for a five-year term at the following
rates:
Alpha
Beta
Moody’s credit rating
Aa
Baa
Fixed-rate borrowing cost
10.5%
12.0%
Floating-rate borrowing cost
LIBOR
LIBOR + 1%
a. Calculate the quality spread differential.
b. Develop an interest rate swap in which both Alpha and Beta have an
equal cost savings in their borrowing costs. Assume Alpha desires floatingrate debt and Beta desires fixed-rate debt. No swap bank is involved in this
transaction.
Review Question: Develop a Swap Contract
› Solution:
› a. The QSD = (12.0% - 10.5%) minus (LIBOR + 1% - LIBOR) = .5%.
› b. Alpha needs to issue fixed-rate debt at 10.5% and Beta needs to issue
floating rate-debt at LIBOR + 1%. Alpha needs to pay LIBOR to Beta.
Beta needs to pay 10.75% to Alpha. If this is done, Alpha’s floating-rate
all-in-cost is: 10.5% + LIBOR - 10.75% = LIBOR - .25%, a .25% savings
over issuing floating-rate debt on its own. Beta’s fixed-rate all-in-cost is:
LIBOR+ 1% + 10.75% - LIBOR = 11.75%, a .25% savings over issuing
fixed-rate debt.
› 10.5%
10.75%
Alpha
›
L+1%
Beta
L