Foreign Exchange Arithmetic Worksheet
For purposes of this worksheet, assume the following exchange rates.
S$/€bid = 1.20
S$/€ask= 1.205
S$/c$bid=.650
S$/c$bid=.651

Are these direct (American) or indirect (European) ?
American, since they describe the dollars per unit of the foreign currency

Suppose an American exporter has just received a payment of € 100,000, how
many dollars will result upon conversion?
The exporter will receive the bid price when the euro are sold. This will yield $120,000=
S$/€bidx100,000=1.20x100,000 .

Suppose an American restaurant budgets $10,000 to restock its wine cellar with
French wine. How many euros does it have to spend.
The restaurant will pay the ask price when it buys the euros. With the $10,000, it can
obtain $8,298.76= 10,000/ S$/€ask=10,000/1.205. [Another way of thinking about this is
to say that the American is selling dollars and so will receive the European bid price.
The European bid is the reciprocal of the American ask, S€/$bid=1/ S€/ffask
=1/1.205=.829876. When the American sells the dollars, the result is 10,000x S€/$bid.]

Suppose a Canadian investor wants to purchase $100,000 worth of U.S. Treasury
bonds. What is the c$ cost of this investment?
The Canadian will be selling C$ to get US dollars and so will receive the bid. It will
require C$153,846 = 100,000/ S$/C$bid=100,000/.650. [Here again, you could work this
by finding the European ask for US dollars.]
For the following problems assume that there are no bid/ask spreads and that
S$/€=1.20 and S$/C$=.60.

What is the quote, in Canadian dollars for euros?
Sc$/€=S$/€/S$/c$=1.20/.60= 2.0

What is the quote in euros for Canadian dollars?
S€/c$=1/Sc$/€=1/2.0=.50

Suppose that you are a currency trader and you see the quotes described above,
but you also notice that in London they are giving quote of S€/c$=.505. Does this
present an arbitrage opportunity, and if so, how much money can you make with
an initial investment of $1,000,000?
Yes, this is an arbitrage opportunity since the rate implied by the cross rate condition,
.50, is different than the rate offered in London.
To figure out how to exploit this opportunity, think about the London trader as offering a
premium number of euros for the Canadian dollars. The trick will be to get Canadian
dollars into that market in order to sell them for the premium number of euros. Here are
the steps:
o Buy Canadian dollars in the US: $1,000,000 =
1,000,000/S$/c$=1,000,000/.6=C$ 1,666,667
o Sell these Canadian dollars in London for
1,166,667xS€/c$=1,166,667x.505=€841,667
o Sell euros in the US for 841,667xS$/€=841,667x.1.20=$1,010,000
Profit of $10,000
For this problem assume that there are no bid/ask spreads and that the following annual
interest rates and exchange rates are available: r$=6%, r£=10%, S$/£=1.60.

What should the one-year forward rate be?
o Fd/f=Sd/f(1+rd)/(1+rf) = 1.6(1.06)/(1.10)=1.5418

If your bank offered a forward contract at F$/£=1.5500 with no other charges or
fees, calculate the arbitrage profits on a deal that involved borrowing or lending
$1,000,000.
The key to this arbitrage is to take advantage of the fact that the bank is offering to
pay $0.0082 more for a British Pound to be delivered in one year than is required
(1.5500-1.5418). This means you need to be in a position to deliver pounds one year
in the future. Here are the steps
o
Borrow $1,000,000 in the U.S. (obligating you to repay $1,060,000) in
one year.
o Use the proceeds from the loan to raise 1,000,000/1.60=£625,000.
o Loan the £625,000 at 10% (that loan will generate £687,500 in one year)
o Sell the amount expected in the forward market for
687,500x1.55=$1,065,625.
Profit = $5,625
Gulfstream Aircraft has entered into a contract to sell a private jet to a
European corporation. The sales price of €20 million will be paid when the
aircraft is delivered in one year. The firm is considering a forward market
hedge, a money market hedge and hedging with a currency option. The
following rates apply.
S0$/€ = 1.3
F1$/€ = 1.2
P (cost of put option) = .02
X (exercise price of put option) = 1.2
Rb$ (dollar bid rate of interest) = 8.0%
Ra$ (dollar asking rate of interest) = 8.5%
Rb€ (euro bid rate of interest) = 10.0%
Ra€ (euro asking rate of interest) = 10.8%
In order to compare each of these hedges prepare a table showing the cash
position in one year if the euro is selling for 1.1, 1.20, 1.3, 1.4 and 1.5
Forward Hedge
Spot
Receivab Forward
Net
le
Contract
1.1 $22.00
$2.00 $24.00
1.2 $24.00
$0.00 $24.00
1.3 $26.00
($2.00) $24.00
1.4 $28.00
($4.00) $24.00
1.5 $30.00
($6.00) $24.00
Spot
Put
Receivab Put
Net
le
Option
1
20
$3.60 $23.60
1.1 $22.00
$1.60 $23.60
1.2 $24.00
$0.00 $24.00
1.3 $26.00
$0.00 $26.00
1.4 $28.00
$0.00 $28.00
1.5 $30.00
$0.00 $30.00
Money Market
Spot
1.1
1.2
1.3
1.4
1.5
Euros Borrowed
€ 18.0505
€ 18.0505
€ 18.0505
€ 18.0505
€ 18.0505
Dollars Loaned
$
23.4657
$
23.4657
$
23.4657
$
23.4657
$
23.4657
Net Dollars Realized
$
25.3430
$
25.3430
$
25.3430
$
25.3430
$
25.3430
Implicit Forward
Rate
1.2671
1.2671
1.2671
1.2671
1.2671