1 (of 24) IBUS 302: International Finance Topic 5-The Market for Foreign Exchange II Lawrence Schrenk, Instructor.

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IBUS 302: International Finance

Topic 5-The Market for Foreign Exchange II

Lawrence Schrenk, Instructor

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Learning Objectives

1. Determine if triangular arbitrage exists and find the arbitrage profit. ▪

2. Explain the forward rate.

3. Calculate forward cross-exchange rates.

4. Calculate the forward premium/discount.▪

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Triangular Arbitrage

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Arbitrage

Arbitrage1. Guaranteed Profit2. No Cost (self-financing trading strategy)3. No Risk

Example: 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 ▪

‘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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Case 1 $1 → £0.52 → €1.33 → $1.10 GAIN $0.10

Triangular Arbitrage: Example

£0.52 €1.33

$1 ≠ $1.10

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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. ▪

Triangular Arbitrage: Example

£0.49 €1.20

$1.00 ≠ $0.90

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Finding Triangular Arbitrage

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 ▪

USD EUR CADUSD 1 0.6898 1.0613EUR 1.4497 1 1.7491CAD 0.9422 0.5717 1

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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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NOTE: Quotation in American Terms Source

Forward Rates (9/11/2008)

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Forward Rates (9/11/2008)Forward Rates F($/£)

9/11/2008

1.6900

1.7000

1.7100

1.7200

1.7300

1.7400

1.7500

1.7600

1 Month 2 Months 3 Months 6 Months 12 Months 2 Years

Bid

Ask

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Bid-Ask Spread (9/11/2008)Spread F($/£)

9/11/2008

0.0020

0.0022

0.0024

0.0026

0.0028

0.0030

0.0032

1 Month 2 Months 3 Months 6 Months 12 Months 2 Years

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Forward Rate Features

Common Maturities 1, 3, 6, 9 and 12 months

Perspectives 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 poundForward Rates F($/£)

9/11/2008

1.6900

1.7000

1.7100

1.7200

1.7300

1.7400

1.7500

1.7600

1 Month 2 Months 3 Months 6 Months 12 Months 2 Years

Bid

Ask

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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 ShortBuy 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

Notes: Both are in American terms. The first currency (¥) goes into the denominator (bottom) The second currency (€) goes into the numerator (top)

22

2

American Terms

American Te

F $/ 1.4497F ( / ) = 157.0980

F ($/ ) 0

E

.¥

00E

r¥ 9228ms

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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.

Holding Period Return

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Premium Formula

,

($ / ) ($ / ) 360

($ / )N

N j

F j S jf

S j days

-

Annualizing Factor ▪

NOTE: N is the normally the number of months, and needs to be converted into days for this calculation.

S($/£)= 1.7544 F1($/£)= 1.7504

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Example: Premium Calculation

11,£

($ / £) ($ / £) 360

($ / £)

F Sf

S days

1,£

1.7504 1.7544 3600.0274 ( 2.74%)

1.7544 30f