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IBUS 302: International FinanceTopic 4-The Bid-Ask Spread and

Cross-Exchange Rates

Lawrence Schrenk, Instructor

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Learning Objectives

1. Explain the bid-ask spread. 2. Calculate cross-exchange rates.3. Calculate cross-exchange bid-ask spread.▪

‘Cancelling Currencies’ I Remember high school physics:

A car is traveling 20 mile per hour and goes for 3 hours, how far has it gone?

You can cancel ‘units’ like algebraic variables to find the correct units of the answer.

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miles20 × 3 hours = 60 mileshour

‘Cancelling Currencies’ II You can cancel currency units the same way:

If S($/£) = 1.4557, how many dollars do you get for £25.00?

Cancel pounds to get dollars.4 (of 24)

$S($/£) = S £

$1.4457 × £25.00 $36.1425£

‘Cancelling Currencies’ III If S($/£) = 1.4557 and S(£/€) = 0.8852, what

is S($/€)?

Cancel pounds to get dollars for euros.

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$ £ $1.4457 × 0.8852 1.2797£ € €

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Bid-Ask Spread

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Bid-Ask Spread Definition: ‘Bid Price’, ‘Ask Price’

Bid price = price to buy Ask price = price to sell

Definition: ‘Spread’ Spread = Ask – Bid

Notation Bid Sb( ) Ask Sa( )

TerminologyS($/£) = 1.7768 ▪

Big Figure: 1.7700 Little Figure: 0.0068 ‘Points’ (or ‘Pips’)

One point is 0.0001 (0.01%) 12 points is 0.0012 (0.12%)

Spread in ‘points’, e.g., a spread of ‘6 points’. 1.7762-68 ▪

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The ‘Market Maker’ Buy and Sell Order not Automatically

Matched Role of Dealers and Inventory Ask price > Bid price

Traders need to sell higher than they buy The spread compensates for costs and risk

commission/brokerage fee

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Managing InventoryS($/£) = 1.7768

Big Figure: 1.7700 Little Figure: 0.0068

6968676665646362

Average Raise Inventory Lower Inventory 63-68 64-69 62-67

The Spread Dealer Costs:

Order Processing Costs Inventory Holding Risks Information Costs of Market Making

Determinants of Spreads: Exchange Rate Volatility (Market Uncertainty) Trading Volume Number of Dealers (Market Competition) Order Sizes

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Spread Characteristics Narrower

New York and London More Competition

Wider High Volatility or Exchange Crisis Rarely Traded Currencies

NOTE: The quoted FX rates are usually the ask/selling prices

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Wholesale vs. Retail Wholesale

Interbank Trading Foreign exchange dealers in different banks in

major financial centers Spread normally 10 points (0.1%)

Retail Corporate Customers Larger Spread

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Dealer Revenues Most wholesale, standard-size transactions

are for $10m or more, so the spread generates profits even though it is very low

A 1 point spread on dollars to pounds S($/£) = 1.90 $10m x £0.0001/$ = £1000 per point Or about $1,900 per point

NOTE: A £ point ≠ $ point.

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Bid AskS($/£) $1.9072 $1.9077 American

S(£/$) £0.5241 £0.5243 European

Bid, Ask, American, European BidAmerican = 1/AskEuropean

BidEuropean = 1/AskAmerican

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Cross-Exchange Rates

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Cross-Exchange Rates ‘Currency against currency’ trade is a non-

dollar to non-dollar trade Cross-exchange rate: the exchange rate

between two non-dollar currencies You can find the cross exchange rate

‘through’ the US dollar.

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Reading the FX Table

Cross-Rates ▪

Directly Traded Cross Rates Directly Traded Cross Rates

Market Quotation Sufficient Volume and Liquidity Expanded in 1980s and ’90s Cross-rates must be internally consistent.

No Arbitrage Triangular Arbitrage EXAMPLES: Euro and Non-Euro European

Currencies, EUR/JPY, AUD/JPY

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Derived Cross Rates Derived (or Implied) Cross Rates

Many currencies pairs are less actively traded Traded through another currency Calculation

‘Vehicle’ Currency More than half of all trades are against $ Lower transactions costs in $ trades €, ¥ also function as lesser vehicle currencies

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Cross-Exchange Rate Formulae: Method 1

How many euro's for one pound? Method 1

Notes: Both are in American terms. The first currency (€) goes into the denominator (bottom) The second currency (£) goes into the numerator (top)NOTE: By ‘first currency’, I mean the first currency in the spot formula, i.e., X, in S(X/Y).

American TS e$/ rmS( / ) = S($

sAmerican

££

T/ )€

€ erms

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Method 1: Example Find S(¥/€)–How many yen for a euro?

If S($/€) = 1.4497 and S($/¥) =0.009228

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

American TermsAmerican Ter

S $/ 1.449¥ 7S( / ) = 157.0980S($/ ) 0.00

€€

¥ 9228ms

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Cross-Exchange Rate Formulae : Method 2 How many euro's for one pound? Method 2

Notes: One in American terms; one in European terms The first currency (€) is in European terms. The second currency (£) is in American terms. The order of multiplication does not matter.NOTE: By ‘first currency’, I mean the first currency in the spot formula, i.e., X, in S(X/Y).

S(€/£) = S $/£ × S(€/$)

$ € €

Ame

= S

rican Terms × Euro

×

pean Term

S = S = S(€/£) £ $ £

s

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Cross-Exchange Rate Formulae : Method 2 Find S(¥/€)–How many yen for a euro?

if S($/€) = 1.4497 and S($/¥) =0.009228

Notes: The first currency is in European terms. The second currency is in American terms. The order of multiplication does not matter. NOTE: When dealing in yen there can be rounding error.

S(¥/€) = S $/€ × S(¥/$) = 1.4497 × 108.3650 = 157.0

American Terms

967

× European T erms

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Bid-Ask Cross-Exchange Rates Using Method 2

Multiply two bids to get a bid. Multiply two asks to get an ask.

Example:

b b bS (¥/€) = S $/€ × S (¥/$)

American Terms × European TermsbS (¥/€) = 1.4497 × 108.3650 = 157.0967