IBUS 302:
International Finance
Topic 4-The Bid-Ask Spread and
Cross-Exchange Rates
Lawrence Schrenk, Instructor
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Learning Objectives
1.
2.
3.
Explain the bid-ask spread.
Calculate cross-exchange rates.
Calculate cross-exchange bid-ask spread.▪
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‘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?
20
m ile s
× 3 h o u rs = 6 0 m ile s
hour

You can cancel ‘units’ like algebraic variables to
find the correct units of the answer.
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‘Cancelling Currencies’ II

You can cancel currency units the same way:
$
S ($ /£ ) = S  
£

If S($/£) = 1.4557, how many dollars do you
get for £25.00?
$ 
1 .4 4 5 7   × £ 2 5 .0 0  $ 3 6 .1 4 2 5
£ 

Cancel pounds to get dollars.
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‘Cancelling Currencies’ III

If S($/£) = 1.4557 and S(£/€) = 0.8852, what
is S($/€)?
$
£
$
1.4457   × 0.8852    1.2797  
£
€
€

Cancel pounds to get dollars for euros.
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Bid-Ask Spread
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Bid-Ask Spread

Definition: ‘Bid Price’, ‘Ask Price’



Definition: ‘Spread’


Bid price = price to buy
Ask price = price to sell
Spread = Ask – Bid
Notation


Bid
Ask
Sb( )
Sa( )
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Terminology
S($/£) = 1.7768 ▪

Big Figure: 1.7700
‘Points’ (or ‘Pips’)



Little Figure: 0.0068
One point is 0.0001 (0.01%)
12 points is 0.0012 (0.12%)
Spread in ‘points’, e.g., a spread of ‘6 points’.

1.7762-68 ▪
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The ‘Market Maker’



Buy and Sell Order not Automatically
Matched
Role of Dealers and Inventory
Ask price > Bid price


Traders need to sell higher than they buy
The spread compensates for costs and risk

commission/brokerage fee
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Managing Inventory
S($/£) = 1.7768
Big Figure: 1.7700 Little Figure: 0.0068
Average
63-68
Raise Inventory Lower Inventory
64-69
62-67
69
68
67
66
65
64
63
62
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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



Wider



New York and London
More Competition
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, Ask, American, European


BidAmerican = 1/AskEuropean
BidEuropean = 1/AskAmerican
Bid
Ask
S($/£)
$1.9072
$1.9077
American
S(£/$)
£0.5241
£0.5243
European
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Cross-Exchange
Rates
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Cross-Exchange Rates



‘Currency against currency’ trade is a nondollar 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 ▪
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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
S ( € /£ ) =

S  $/ £  A m erican T e rm s
S ($ / € ) A m erican T erm s
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).
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Method 1: Example

Find S(¥/€)–How many yen for a euro?

If S($/€) = 1.4497 and S($/¥) =0.009228
S (¥ / € ) =
S  $/ €  A m erican T erm s
S ($/ ¥ ) A m erican T er m s


1.449 7
 157.0980
0.00 9228
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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Cross-Exchange Rate
Formulae : Method 2


How many euro's for one pound?
Method 2
S ( € /£ ) = S  $ /£  × S ( € /$ ) A m e rica n T e rm s × E u ro p e a n T e rm s
$
€
€
= S   × S   = S   = S ( € /£ )
£
$
£

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).
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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
S (¥ / € ) = S  $ / €  × S (¥ /$ ) = 1 .4 4 9 7 × 1 0 8 .3 6 5 0 = 1 5 7 .0 9 6 7
A m e rica n T e rm s × E u ro p e a n T e rm s

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.
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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
S (¥ / € ) = S
b
 $ / €  × S (¥ /$ )
b
A m e rica n T e rm s × E u ro p e a n T e rm s
b
S (¥/ € ) = 1.4497 × 108.3650 = 157.0967
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