Class Notes
International Finance
Spot Rate – The price of a currency in terms of another currency for a trade today.
Forward Rate – The price of a currency in terms of another currency for a trade agreed
upon today but to be executed at a specified time in the future (usually 30, 60, 90, 180 or
360 days).
Direct Quote (American Quote) – Domestic Currency/Foreign Currency
The number of dollars needed to buy one unit of the foreign currency.
Indirect Quote (European Quote) – Foreign Currency/Domestic Currency
The number of units of a foreign currency needed to buy one dollar.
Direct and indirect quotes are both correct. They are reciprocals of each other.
Example: US and European Currencies:
1.23 $/€ is the same as .813 €/$
Think of a currency as a commodity.
Bananas can be $0.50/pound or 2 lbs. For a dollar
Price of a dollar = € .813
Price of a euro = $1.23
Note that the currency in the denominator is the one being priced.
If you have dollars and want euros, you are selling dollars and buying euros. Both mean
the same thing.
If you have € and want $, you sell € and buy dollars.
Suppose you have $5.00. How many euros is it worth if the XR is 1.23 $/€ ? (multiply or
divide?)
Direct quote:
$5 1.23 $/€ = x - note that the $ won’t cancel out
You must invert which means using an indirect quote or dividing.
$5 ÷ 1.23 $/€ = $5 1/1.23 €/$ = $5 . 813 €/$ = € 4.065
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Suppose you have € 30 and want dollars?
€ 30
1.23 $/€ = $36.90
Cross Exchange Rate – one foreign currency per unit of another foreign currency
Example:
1.23 $/€
1.81 $/£
What is the cross-rate between the euro and the pound?
Just multiply so as to cancel out $.
1.23 $/€
1.81 $/£ - can’t do it – must divide or invert.
1.23 $/€ ÷ 1.81 $/£ = 1.23 $/€
1/1.81 $/£ = 0.68 £/€
If you want €/£, just take the reciprocal = 1.47 €/£
Unfortunately, there is not one exchange rate, but two – the bid and the ask.
Ask > Bid
Ask – Price a dealer (bank) will sell you units of a currency for. This is the rate you get if
you want to buy.
Bid – Price a dealer (bank) will pay you for your currency. This is the rate you get if you
want to sell.
Example:
Indirect Quotes
Ask – 1.29 SF/$
Bid – 1.28 SF/$
Direct Quotes
Ask – .78125 $/SF
Bid – .7752 $/SF
Note that the Bid in $ = Ask in SF
and the Bid in SF = Ask in $
Remember that the currency in the denominator is the one being priced, and that the ask
is the price you will buy that currency at and the bid is the price you will sell that
currency at.
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Example: you go to the bank and see direct quotes of:
Ask: .0091 $/¥
Bid: .0090 $/¥
You have $150 that you want to convert to yen. How many yen will you get?
You want to buy yen at the price of .0091 $/¥
Or
You want to sell Dollars at the price of 1/.0091 ¥/$
$150 ÷ .0091 $/¥ = ¥ 16,483.5
You change your mind and now want to convert back. How much will you get?
You want to sell yen at a price of .0090 $/¥
Or
You want to buy Dollars at a price of 1/.0090 ¥/$
¥ 16,483.5 . 0090 $/¥ = $148.35
Note that you lost $1.65
This is a loss of 1.1% on $150
The Bid-Ask spread can be computed in percentage terms:
Spread = Ask – Bid
Ask
With the previous example: .0091 - .0090
.0091
= 1.1% = amount we lost on a round trip
So the spread is the transaction cost for a round-trip transaction.
If you are transacting greater amounts of a currency, the spread decreases
If you are dealing with a less frequently traded currency, the spread increases
Forward Rate – The price of a currency in terms of another currency for a trade agreed
upon today but to be executed at a specified time in the future (usually 30, 60, 90, 180 or
360 days).
The purpose is to lock in an exchange rate and thus eliminate exchange rate risk.
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XR risk – the risk that the XR may move in an unfavorable direction.
People (and corporations) are risk averse, so they often prefer a certain forward rate to a
risky future spot rate.
Example:
You are a buyer for Circuit City and you have placed an order for 10,000 Sony
televisions for your stores for Christmas. You must pay Sony in six months when they are
delivered, and you must pay in Yen. The agreed upon price is ¥ 300 million. It is locked
in.
The current XR is .008 $/¥ = $2,400,000
What if the yen appreciates against the dollar over the next six months? What if the XR
goes to .010 $/¥ ?
Note: Make sure that you see that when the yen appreciates, the XR goes up, because the
yen now buys more dollars – or – it takes more dollars to buy a yen.
¥ 300 million . 010 $/¥ = $ 3,000,000
It now costs you $600,000 more than you thought.
Of course, the yen could depreciate too, but you don’t know what it will do.
Suppose you can enter into a forward contract to trade dollars for yen in 180 days at a
rate of .0085 $/¥ ?
You agree to sell dollars (buy yen) in 180 days at 117.65 ¥/$
You buy ¥ 300 million at .0085 $/¥ for $2,550,000
Who do you buy it from? A bank.
Forward contracts are almost always with Banks
They are individually tailored
There is no money exchanged at the time of the agreement
If Forward Rate > Spot Rate there is a forward premium
If Forward Rate < Spot Rate there is a forward discount
In our example, Spot Rate = .0080 $/¥
Forward Rate = .0085 $/¥
There is a forward premium since Forward > Spot
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Premiums and discounts are computed on an annual basis.
For Direct Quotes:
Premium (discount) = Forward Rate – Spot Rate 
360
Spot Rate
Length of Forward Contract (in days)
= .0085 - .0080  360
.0080
180
= .125
= 12.5%
For an Indirect Quote:
Premium (discount) = Spot Rate – Forward Rate 
360
Forward Rate
Length of Forward Contract (in days)
Note that a negative value would be a discount.
What determines the forward rate?
If you are a bank, and you engage in trades in both directions, how will you set the
forward rate?
Note: The forward rate is not the same thing as the future spot rate.
You will want the forward rate to be close to what you expect the spot rate to be at that
time. Some thus feel that the forward rate is an unbiased predictor of the expected future
spot rate – but it is not. Meaning you can’t look at today’s forward rate and say that in 6
months I’ll exchange currency on the spot market at that rate.
So how exactly is the forward rate determined? An example may help.
Suppose the spot rate for CD (Canadian dollars) is .73 $/CD
The 6 mo. forward rate for CD is also .73 $/CD
The U.S. interest rate is 5% (per year)
The Canadian interest rate is 5.5%
What can you do?
1.
2.
3.
4.
Borrow $100 at 5% in the U.S.
Convert it to CD: $100  .73 $/CD = CD 136.99
Invest it in Canada at 5.5% for six months
Enter into a forward contract to sell CD 140.76 at .73 $/CD in six months
Six Months from now:
1. Your CD 136.94 has grown to CD 140.76 136.99 (1 + .055/2) = 140.76
2. Convert the CD to $ thru your forward contract CD140.76  .73 $/CD = $102.75
3. Pay off your debt. $100 (1 + .05/2) = $102.50
4. You have $0.25 profit
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You made $.025 in 6 months. But notice that you didn’t need any investment – just the
ability to borrow $100.
You can make $25,000 if you borrow $10 million and $250,000 if you borrow $100
million.
This is arbitrage – making a guaranteed profit with no upfront investment.
This condition will not hold.
As everyone buys CD in the spot market, the CD appreciates which increases the XR.
As everyone sells CD in the forward market, the forward rate goes down.
In equilibrium, the following relationship must hold:
(1 + i) = F(0,1)
(1 + i*) S(0)
where i = domestic int. rate and i* = foreign int. rate
and we are using direct quotes for the forward and spot rates
In our example: F = .73 $/CD  (1 + .05/2)
(1 + .055/2)
= .728224 $/CD
So CD should be selling forward at a discount. If this is the forward rate, and you try to
arbitrage, when you convert back your CD to $, you will get CD 140.76  .728224 =
$102.50 which will just pay off the U.S. loan
This is called Interest Rate Parity. The country with the higher interest rates will have
its currency selling forward at a discount. If Interest Rate Parity exists, covered interest
arbitrage will not be possible. The above example was covered because we used the
forward rate to “cover” our currency conversion in six months – no risk.
Covered interest arbitrage involves borrowing in the home currency, converting it to the
foreign currency, and investing it at a higher interest rate, taking out a forward contract to
convert it back to the home currency at maturity, paying off the home loan and ending up
with a profit.
Transaction costs, risk differences and taxes mean that the forward rate doesn’t have to
exactly equal the spot times the interest rate ratio, but it must be close enough so that an
arbitrage profit cannot be made.
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Triangular Arbitrage
Suppose you observe the following exchange rates:
0.8155 €/$
1.3235 CD/$
0.635 €/CD
The “fair“ crossrate is 0.8155 €/$ = 0.61617 €/CD
1.3235 CD/$
There is a triangular arbitrage opportunity here.
At 0.635 €/CD, the CD is more expensive than it should be and the € is cheaper than it
should be – because the CD costs € 0.635 rather than the € 0.616 it “should” cost.
Arbitrage: Buy the cheap currency and sell the expensive one
Buy € and sell CD
Start with $1,000,000 and convert it into CD. Note that you must convert the $ into CD
so that you can sell the CD and buy euros. If you had bought euros with your $, you
would have then had to sell the cheap euros and bought the expensive CD – resulting in a
loss.
If you start with $1 million, you earn a riskless instant profit of $30,561.
Note that we simplified this by not showing bids and asks.
What causes arbitrage to disappear?
If everyone sells CD and buys €, the cross XR will adjust to the fair crossrate. Dealers
who see all their order flow going in one direction will adjust their quotes.
Since there is not just one price for a currency, but two, let’s look at triangular arbitrage
with both a bid and and an ask price for each currency.
We observe the following indirect quotes:
Bid
1.25 SF/$
.812 €/$
1.58 SF/€
Ask
1.28 SF/$
.818 €/$
1.60 SF/€
This is the same as these direct quotes:
Bid
0.78125 $/SF
1.2225 $/€
0.625 €/SF
Ask
0.80 $/SF
1.2315 $/€
0.6329 €/SF
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What are the “fair” crossrates?
Bid: 1.25 SF/$ = 1.539 SF/€
.812 €/$
Ask: 1.28 SF/$ = 1.565 SF/€
.818 €/$
Note that the true crossrates (bid = 1.58 and ask = 1.60) are both higher than the fair
rates.
So one euro should (cost) be worth 1.539 or 1.565 SF but it actually costs 1.58 or 1.60 SF
So the euro is expensive and the SF is cheap
Buy the cheap SF and sell the expensive euro
1. Start with $1,000
Sell $ at .812 €/$ or buy euros at 1.2315 $/€
End up with € 812
2. Sell euros at 1.58 SF/€ or buy SF at 0.6329 €/SF
End up with SF 1,282.96
3. Sell SF at 0.78125 $/SF or buy $ at 1.28 SF/$
End up with $1,002.31
You made $2.31 through Triangular Arbitrage
This triangular arbitrage will tend to go away because:
Indirect quotes:
Everyone sells dollars and buys euros
so bid price of dollars goes down from .812 €/$
Everyone sells euros and buys SF
Everyone sells SF and buys dollars
so ask price of dollars goes up from 1.28 SF/$
If SF/$ goes up and €/$ goes down,
the “fair” crossrate of 1.25 SF/$ = 1.539 SF/€ must go up
.812 €/$
At the same time, the actual cross rate of 1.58 SF/€ goes down.
So the “fair” crossrate will equal the actual cross rate in equilibrium.
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Locational Arbitrage
Remember that you (you are not a dealer) always buy at the ask and sell at the bid.
If Dealer A has its ask lower than the bid of Dealer B, you can do locational arbitrage.
Example:
Dealer A
Bid
Ask
2680 Peso/$
2683 Peso/$
Dealer B
Bid
2685 Peso/$
Ask
2688 Peso/$
Buy dollars from A and sell them to B
But with every one buying dollars from A, his ask price will go up
And with everyone selling dollars to B, his bid price will go down
So in equilibrium, A’s ask will be > B’s bid
Purchasing Power Parity and the Law of One Price
The law of one price says that the same good will cost the same amount everywhere. If
not, there is an arbitrage opportunity.
Buy the good one place and sell it in another place where the price is higher.
This means that PD = SD/F (direct)  PF Note: D = Domestic and F = Foreign
The price of a good domestically is the same as its price on a foreign market, adjusted for
the exchange rate.
This presumes frictionless markets
In reality, there are transportation costs, goods are not always identical, differences in
tastes in different countries, and taxes and tariffs.
Test of PPP – The Big Mac Standard
Can you buy Big Macs in the Phillipenes, take them to Switzerland, and sell them
for a profit?
Even though The Big Mac does not have the same price everywhere, it is not
arbitragable.
Absolute PPP deals with specific goods such as a Big Mac (usually a collection of goods
though).
Relative PPP deals with changes in prices (inflation or deflation).
Relative PPP says that prices in different markets should change at the same rate, and that
unequal changes in prices will be reflected in their exchange rate.
1 + domestic inflation rate / 1 + foreign inflation rate = 1 + change in exchange rate
(1 + ΠD) = St+1
(1 + ΠF)
St
Or, (1 + ΠD) = 1 + ΔSD/F
(1 + ΠF)
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Tests have shown that relative PPP does tend to hold true in the long-run much better
than in the short run.
International Fisher Effect
The Fisher effect says that nominal (observed) interest rates are equal to the real interest
rate plus the expected inflation rate. Actually, the formula is:
1 + real rate
=
1 + nominal rate
1 + inflation rate
Investors are only concerned with the real rate and will invest where it is highest, and
borrow where it is lowest. In order to avoid arbitrage therefore, every country’s real rate
must be equal.
This means that differences between two countrys’ nominal interest rates must be entirely
due to differences in expectations about their relative rates of inflation.
The spot exchange rate should change in an amount equal to but in the opposite direction
from the difference in interest rates between two countries.
The percentage change in the spot rate should equal the percentage relative change in
interest rates or the percentage relative change in inflation.
Hedging Transaction Exposure
Suppose Daimler Benz wants to build a new plant in Germany and they open bids to the
construction firms with the bids to be made in Euros.
A U.S. firm enters its bid as 100 million Euros which is $122 million at a spot rate of
1.22 $/€.
One month later, Daimler Benz informs the U.S. firm that it has won the bid. However,
by now the XR is at 1.15 $/€ so the $100 million euros to be paid is now worth $115
million.
The U.S. firm takes 8 months to build the plant and D-B pays them 3 months after that.
This means that the XR can move even more. This is an example of transaction exposure.
One way to eliminate transaction exposure is to match your assets and liabilities in the
same currency. In this case, the U.S. firm could plan to pay in euros for building supplies
and workers’ wages, so when the euro depreciates, the dollar cost of the building goes
down too.
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If a firm chooses to hedge its transaction exposure, there are three ways it can do so that
we will examine.
1. Forward Contract Hedge
2. Money Market Hedge
3. Options Hedge
With forward contracts, if you have an asset such as a receivable in a foreign currency,
you must create a liability – meaning you contract to sell 100 million euros in one year.
This locks in a rate and guarantees that you will get a certain amount of dollars for the
100 million euros you will be paid.
Money market hedges use interest rates. Again, you want to create a liability to offset
your asset. This means you must create a situation where you owe 100 million euros in a
year.
Borrow ____ euros now so that the amount due with interest will be 100 million euros.
Assume that the interest rate is 5%. Borrow the present value of 100 million euros
discounted at 5%.
PV = FV
(1+r)t
=
€ 100 million
1.05
= € 95.238 million
Convert the € 95.238 million to dollars at the current spot rate to lock-in your payment.
There is no risk. In one year you will be paid 100 million euros by D-M and you use that
to pay what you borrowed.
With an options hedge, you purchase an option to sell your 100 million euros for a
specified XR. In this case, you would buy a put (an option to sell).
If the euro depreciates, you exercise the option to sell at the high price.
If the euro appreciates, you tear up the option and sell at the spot rate.
If your transaction exposure is a liability in one year rather than an asset, you want to do
things just a bit differently.
With the forward contract, you want to create an asset, so you buy the foreign currency
forward.
With the money market hedge, you also want to create an asset so you:
Convert dollars to euros and invest them for one year. Then use the proceeds to pay off
the liability.
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You lock-in at the spot rate of converting today.
If you don’t have the dollars today to convert, you need to borrow at the local interest
rate.
With options, you need to buy a call (an option to buy). This gives you the option to buy
the foreign currency at a locked-in price if need be to pay the liability.
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Currency Swaps
What often motivates a currency swap is two firms wanting to borrow in different
currencies and each has a comparative advantage in the currency that the other wants to
borrow in.
Example:
Firm A wants to borrow in pounds
Firm B wants to borrow in dollars
(perhaps they want to borrow in these currencies to offset existing receivables)
These are the interest rates they can borrow at:
A
B
Dollars
8.0%
10.0%
Pounds
11.6%
12.0%
Note that A is more credit-worthy than B. It can borrow at a lower rate in either currency.
However, A can borrow at 2% below B in dollars, but only 0.4% below B in pounds.
Thus A has an absolute advantage in both currencies, but a comparative advantage in
dollars.
B has a comparative advantage in pounds.
The swap will only work if each firm wants to borrow in the currency where the other
enjoys a comparative advantage.
The potential gain from the swap is the difference between the differences in the
borrowing rates.
A
B
Dollars
8.0%
10.0%
2.0%
Pounds
11.6%
12.0%
0.4%
2.0% - 0.4% = 1.6% = potential gain
The potential gain is to be divided up among Firm A, Firm B, and the financial
intermediary who sets up the swap.
The financial intermediary is usually a large commercial bank or an investment bank. It
acts as a dealer.
Suppose they decide that the potential gain is to be divided up as follows:
Firm A: 0.6%
Firm B: 0.6%
Bank: 0.4%
1.6%
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Designing the swap
Firm A wants to borrow in pounds, but has a comparative advantage in dollars.
Firm B wants to borrow in dollars, but has a comparative advantage in pounds.
Each firm should borrow where they have a comparative advantage and swap with the
other so that they end up with the currency they wanted to borrow in the first place.
This is an exchange of loans.
The face value of each loan must be the same at the current spot rate.
The face value is called The Notional Principal.
For example if the spot rate is 1.5 dollars/pound, the notional principal is 15 million
dollars or 10 million pounds.
1. Firm A borrows 15 million dollars at 8.0% from its lender
Firm B borrows 10 million pounds at 12.0% from its lender
2. Firms A and B each give the principal to the bank which passes it through to the
other party.
3. Firm A pays interest to the bank on pounds at 11.0%
Firm B pays interest to the bank on dollars at 9.4%
4. The bank gives firm A 8.0% on 15 million dollars to pay its lender
The bank gives firm B 12.0% on 10 million pounds to pay its lender
Firm A pays 11% for pounds instead of the quoted rate of 11.6%
Firm B pays 9.4% for dollars instead of the quoted rate of 10.0%
The bank:
Receives 11% on pounds
Receives 9.4% on dollars
Pays 12% on pounds
Pays 8% on dollars
Thus the bank has a net of +0.4%
The risk to the bank is if the dollar depreciates and the pound appreciates
There is no currency risk to Firms A or B
If firm A stops paying the bank the 11% interest on pounds, the bank will stop paying
firm A the 8% interest on dollars, so the default risk is reduced for the bank.
Firm A swapped a 15 million dollar loan for a 10 million pound loan
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Firm B swapped a 10 million pound loan for a 15 million dollar loan
Each company got the loan they wanted at a rate that was lower than they could have
gotten on their own.
The bank makes ($15 mill.) (0.4%) = $60,000 for arranging the swap and bearing some
XR risk.
Some banks will do swaps even if they can’t find a counter party right away.
The two firms could have swapped without the bank, but then they bear the risk that if the
XR moves in a way that is favorable for them (and unfavorable for the counter-party), the
other company will stop making payments.
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