IBUS 302:
International Finance
Topic 5-The Market for
Foreign Exchange II
Lawrence Schrenk, Instructor
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Learning Objectives
1.
2.
3.
4.
Determine if triangular arbitrage exists and
find the arbitrage profit. ▪
Explain the forward rate.
Calculate forward cross-exchange rates.
Calculate the forward premium/discount.▪
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Triangular Arbitrage
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Arbitrage
Arbitrage

1.
2.
3.
Example:





Guaranteed Profit
No Cost (self-financing trading strategy)
No Risk
IBM $100 in New York and $102 in Chicago. ▪
How do you take advantage of the opportunity?
What is the arbitrage profit?
Law of One Price ▪
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‘Arbitrage’ Types



Pure Arbitrage: No risk nothing and earn
more than the riskless rate
Near Arbitrage: Assets are identical or
almost, but there is no guarantee of profit
Speculative Arbitrage:

Investors take advantage of what they see as
mispriced and similar (though not identical) assets
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Triangular Arbitrage

Convert money through three currencies
$ → £→ € → $

Arbitrage opportunity if the ending dollar value
does not equal the beginning dollar value.
$ ≠ $
£
€
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Triangular Arbitrage: Example
Case 1


$1 → £0.52 → €1.33 → $1.10 GAIN $0.10
$1 ≠ $1.10
£0.52
€1.33
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Triangular Arbitrage: Example
Case 2 (using different FX rates)



$1 → £0.49 → €1.20 → $0.90 LOSS ($0.10) ▪
If you get a loss of ($0.10), just go the opposite
direction beginning with $0.90 and you will gain
$0.10. ▪
$1.00 ≠ $0.90
£0.49
€1.20
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Finding Triangular Arbitrage
USD
USD
EUR
CAD
EUR
1
1.4497
0.9422
CAD
0.6898
1
0.5717
1.0613
1.7491
1
Is there an arbitrage opportunity?





$ → € → C$ → $ ▪
$ → € : $1.00 x 0.6898 = €0.6898
€ → C$: €0.6898 x 1.7491 = C$1.2065
C$ → $: C$1.2065 x 0.9422 = $1.1368
Arbitrage Profit of $0.1368


$1.00 x 0.6898 x 1.7491 x 0.9422 = $1.1368 ▪
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The Forward Market
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The Forward Market





Buying and selling ‘forward’, i.e., into the
future.
Transfer purchasing power across currencies
and across time
Market expectations
Forward markets are insurance markets for
hedging or eliminating currency risk.
Online Data: OZForex
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Terminology



Forward Rate: The exchange rate to trade
sometime in the future.
Forward Contract: A customized contract
settled today for future delivery/receipt of FX.
Futures Contract: A standardized contract
settled today for future delivery/receipt of FX.
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Forward Rates (9/11/2008)
NOTE: Quotation in American Terms Source
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Forward Rates (9/11/2008)
Forward Rates F($/£)
9/11/2008
1.7600
1.7500
1.7400
1.7300
Bid
Ask
1.7200
1.7100
1.7000
1.6900
1 Month
2 Months
3 Months
6 Months 12 Months
2 Years
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Bid-Ask Spread (9/11/2008)
Spread F($/£)
9/11/2008
0.0032
0.0030
0.0028
0.0026
0.0024
0.0022
0.0020
1 Month
2 Months
3 Months
6 Months
12 Months
2 Years
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Forward Rate Features

Common Maturities


Perspectives



1, 3, 6, 9 and 12 months
Direct versus Indirect
American versus European
Limited to Major Currencies
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Forward Rate Notation


Notation

FN(j/k)

number of j needed to buy 1 k in N months
Difference from Spot Rate Notations



‘F’ not ‘S’
N because you always need to specify the time of
a forward rate
NOTE: S(j/k) = F0(j/k)
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Premium versus Discount

Premium: A currency is trading at a premium
when (in American terms) the forward rate is
increasing.


Market Expectation: The currency will appreciate
and the US dollar will depreciate.
Discount: A currency is trading at a discount
when (in American terms) the forward rate is
decreasing.

Market Expectation: The currency will depreciate
and US dollar will appreciate.
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Example: Trading at a
Discount


Pound is trading at a discount to the dollar
Market expects dollar to appreciate with
respect to the pound
Forw ard Rates F($/£)
9/11/2008
1.7600
1.7500
1.7400
1.7300
Bid
Ask
1.7200
1.7100
1.7000
1.6900
1 Month
2 Months
3 Months
6 Months
12 Months
2 Years
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Market Expectations




Psychology–The ‘Black Box’
Forward Rates are only market expectations
(unless you lock them in with a contract).
All prices, rates, etc. are based on the current
‘information set’.
New information (‘News’)
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Long versus Short Positions
Long
Short
Buy Stock
Short Sell Stock
Buy a Forward Contract
Sell a Forward Contract
Buy an Option
Sell an Option
Buy a Bond
Sell a Bond
Lend
Borrow
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Speculation versus Hedging



Speculation: Taking a position that increases
the risk of your portfolio.
Hedging: Taking a position that decreases
the risk of your portfolio.
In practice, the distinction can be blurred.
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Forward Cross-Exchange
Rates


Same as spot cross-exchange rates.
Find F2(¥/€)–How many yen for a euro in two months?

If F2($/€) = 1.4497 and F2($/¥) =0.009228
F2 (¥/E) =

F2  $/E  American Terms
F2 ($/¥) American Terms

1.4497
 157.0980
0.009228
Notes:



Both are in American terms.
The first currency (¥) goes into the denominator (bottom)
The second currency (€) goes into the numerator (top)
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Swaps versus Forward
Transactions

Forward Transaction



Sale of currency in the future
Uncovered
Swap Transaction



Sale (purchase) now and forward purchase (sale)
in the future
Hedged
More on swaps later.
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Forward Premium/Discount


Premium or discount (f) as an annualized
percentage change from the spot rate.
Notation



fN,j is the forward premium at N of currency j in
American terms.
fN,$ is the forward premium at N of US dollars in
European terms.
Essentially, this gives you, in percentage
terms, how much the forward rate is expected
to moves from the spot annually.
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Premium Formula
fN , j
FN ($ / j )  S($ / j ) 360


S($ / j )
days
Holding Period
Return
Annualizing
Factor ▪
NOTE: N is the normally the number of months, and
needs to be converted into days for this calculation.
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Example: Premium Calculation


S($/£)= 1.7544
F1($/£)= 1.7504
f1,£
f1,£
F1($ / £)  S($ / £) 360


S($ / £)
days
1.7504  1.7544 360


 0.0274 ( 2.74%)
1.7544
30
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