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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.▪

2 (of 24)
‘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?

miles
20       × 3 hours = 60 miles
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?
\$
1.4457   × £25.00  \$36.1425
£
   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’
   Bid price = price to buy
   Ask price = price to sell
   Definition: ‘Spread’
   Spread = Ask – Bid
   Notation
   Bid     S b( )
   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 Inventory
S(\$/£) = 1.7768
Big Figure: 1.7700 Little Figure: 0.0068
Average   Raise Inventory Lower Inventory
63-68        64-69           62-67
69
68
67
66
65
64
63
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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, 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 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 ▪

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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  \$/£  American Terms
S( € /£) =
S(\$/ € ) American Terms

   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  \$/ €  American Terms
1.4497
S(¥/ €) =                                157.0980
S(\$/¥) American Terms 0.009228
   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(€/\$) American Terms × European Terms
\$     €     €
= 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(¥/\$) = 1.4497 × 108.3650 = 157.0967
American Terms × European Terms
   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.

24 (of 24)
Bid-Ask
Cross-Exchange Rates
   Using Method 2
   Multiply two bids to get a bid.
   Multiply two asks to get an ask.
   Example:

Sb (¥/€) = Sb  \$/€  × Sb (¥/\$)
American Terms × European Terms
Sb (¥/€) = 1.4497 × 108.3650 = 157.0967

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