### PowerPoint Slides 4

```IBUS 302:
International Finance
Cross-Exchange Rates
Lawrence Schrenk, Instructor
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Learning Objectives
1.
2.
3.
Calculate cross-exchange rates.
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‘Cancelling Currencies’ I
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Remember high school physics:
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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
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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 price = price to buy
Ask price = price to sell
Notation
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Bid
Sb( )
Sa( )
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Terminology
S(\$/£) = 1.7768 ▪
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Big Figure: 1.7700
‘Points’ (or ‘Pips’)
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Little Figure: 0.0068
One point is 0.0001 (0.01%)
12 points is 0.0012 (0.12%)

1.7762-68 ▪
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The ‘Market Maker’
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Buy and Sell Order not Automatically
Matched
Role of Dealers and Inventory
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The spread compensates for costs and risk
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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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Dealer Costs:
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Order Processing Costs
Inventory Holding Risks
Information Costs of Market Making
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Exchange Rate Volatility (Market Uncertainty)
Number of Dealers (Market Competition)
Order Sizes
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Narrower
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Wider
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New York and London
More Competition
High Volatility or Exchange Crisis
NOTE: The quoted FX rates are usually the
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Wholesale vs. Retail
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Wholesale
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Foreign exchange dealers in different banks in
major financial centers
Retail
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Corporate Customers
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Dealer Revenues
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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
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S(\$/£) = 1.90
\$10m x £0.0001/\$ = £1000 per point
NOTE: A £ point ≠ \$ point.
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Bid
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
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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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Cross-Rates ▪
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Market Quotation
Sufficient Volume and Liquidity
Expanded in 1980s and ’90s
Cross-rates must be internally consistent.
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No Arbitrage
Triangular Arbitrage
EXAMPLES: Euro and Non-Euro European
Currencies, EUR/JPY, AUD/JPY
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Derived Cross Rates
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Derived (or Implied) Cross Rates
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Many currencies pairs are less actively traded
Calculation
‘Vehicle’ Currency
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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
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How many euro's for one pound?
Method 1
S ( € /£ ) =
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S  \$/ £  A m erican T e rm s
S (\$ / € ) A m erican T erm s
Notes:
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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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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
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Find S(¥/€)–How many yen for a euro?
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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:
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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

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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
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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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Cross-Exchange Rates
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Using Method 2
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Multiply two bids to get a bid.