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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.▪
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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?
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
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‘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 $36.1425
£
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‘Cancelling Currencies’ III
If S($/£) = 1.4557 and S(£/€) = 0.8852, what is S($/€)?
Cancel pounds to get dollars for euros.
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$ £ $1.4457 × 0.8852 1.2797
£ € €
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Bid-Ask Spread
Definition: ‘Bid Price’, ‘Ask Price’ Bid price = price to buy Ask price = price to sell
Definition: ‘Spread’ Spread = Ask – Bid
Notation Bid Sb( ) Ask Sa( )
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Terminology
S($/£) = 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
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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 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.
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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
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