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IBUS 302: International Finance
Topic 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 miles
hour
‘Cancelling Currencies’ II
You can cancel currency units the same way:
If S($/£) = 1.4557, how many dollars do you get for £25.00?
Cancel pounds to get dollars.
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$S($/£) = S
£
$1.4457 × £25.00 $36.1425
£
‘Cancelling Currencies’ III
If S($/£) = 1.4557 and S(£/€) = 0.8852, what is S($/€)?
Cancel pounds to get dollars for euros.
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$ £ $1.4457 × 0.8852 1.2797
£ € €
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Bid-Ask Spread
Definition: ‘Bid Price’, ‘Ask Price’ Bid price = price to buy Ask price = price to sell
Definition: ‘Spread’ Spread = Ask – Bid
Notation Bid Sb( ) Ask Sa( )
Terminology
S($/£) = 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
69
68
67
66
65
64
63
62
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 Ask
S($/£) $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
‘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.
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$/ rmS( / ) =
S($
s
American
££
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 Terms
American Ter
S $/ 1.449¥
7S( / ) = 157.0980
S($/ ) 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