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					           IBUS 302:
International Finance
Topic 4-The Bid-Ask Spread and
         Cross-Exchange Rates

   Lawrence Schrenk, Instructor



                                  1 (of 24)
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.


                                                       3 (of 24)
‘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  $36.1425
             £
   Cancel pounds to get dollars.
                                           4 (of 24)
‘Cancelling Currencies’ III
   If S($/£) = 1.4557 and S(£/€) = 0.8852, what
    is S($/€)?

       $          £          $
1.4457   × 0.8852    1.2797  
       £          €          €
   Cancel pounds to get dollars for euros.

                                              5 (of 24)
Bid-Ask Spread




                 6 (of 24)
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( )

                                           7 (of 24)
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 ▪

                                                  8 (of 24)
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


                                                    9 (of 24)
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
     62                                               10 (of 24)
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
                                                    11 (of 24)
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

                                             12 (of 24)
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


                                                    13 (of 24)
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.

                                              14 (of 24)
Bid, Ask, American, European
   BidAmerican = 1/AskEuropean
   BidEuropean = 1/AskAmerican
                     Bid      Ask
          S($/£)   $1.9072   $1.9077   American




          S(£/$)   £0.5241   £0.5243   European
                                                  15 (of 24)
Cross-Exchange
         Rates




                 16 (of 24)
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.



                                             17 (of 24)
Reading the FX Table




                       Cross-Rates ▪

                                       18 (of 24)
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

                                                     19 (of 24)
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

                                                     20 (of 24)
    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).


                                                                                        21 (of 24)
    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)



                                                           22 (of 24)
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).
                                                                                      23 (of 24)
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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