Certain Selected Problems
Chapter 7
• 1. The $: € exchange rate is €1 = $0.95,
and the €/SFr exchange rate is SFr 1 =
€0.71. What is the SFr/$ exchange rate?
• Answer. SFr1 = €0.71 x 0.95 = $0.6745.
• 2. Suppose the direct quote for sterling in
New York is 1.1110-5. What is the direct
quote for dollars in London?
• Answer. The direct quote for the dollar in
London is just the reciprocal of the direct
quote for the pound in New York or
1/1.1115 - 1/1.1110 = 0.8997-0.9001.
• 3. Using the data in Exhibit 7.5, calculate
the 30-day, 90-day, and 180-day forward
discounts for the Canadian dollar.
ANSWER. Here are the relevant rates for the Canadian dollar:
Spot:
C$1 = $0.7545
30-day forward:
C$1 = $0.7536
90-day forward:
C$1 = $0.7520
180-day forward:
C$1 = $0.7501
• The 30-day forward discount
is:[($0.7536 - $0.7545)/$0.7545] x 12 =
1.43%
• The 90-day forward discount is:
[($0.7520 - $0.7545)/$0.7545] x 4 = 1.33%
• The 180-day forward discount
is:[($0.7501 - $0.7545)/$0.7545] x 2 =
1.17%
• 4. An investor wishes to buy euros spot
(at $0.9080) and sell euros forward for 180
days (at $0.9146).
• a. What is the swap rate on euros?
• b. What is the premium on 180-day euros?
• Answer. A premium of 66 points.
• Answer. The 180-day premium is
(0.9146 - 0.9080)/0.9080 x 2 = 1.45%.
• 7. Suppose the euro is quoted at
0.7064-80 in London, and the pound
sterling is quoted at 1.6244-59 in Frankfurt.
• a. Is there a profitable arbitrage situation?
Describe it.
• Answer. Sell euros for £0.7080/€ in
London. Use the pounds to buy euros for
€1.6244/£ in Frankfurt. This is equivalent
to buying pounds for £0.6156. There is a
net profit of £0.0924 per pound bought and
sold–a percentage yield of 13.05%
(0.0924/0.7080).
• b. Compute the percentage bid-ask
spreads on the pound and euro.
• Answer. The percentage bid-ask spreads
on the pound and euro are calculated as
follows:
• £ bid-ask spread = (1.6259 1.6244)/1.6259 = 0.09%
• euro bid-ask spread = (0.7080 0.7064)/0.7080 = 0.23%
•
8. As a foreign exchange trader at
Sumitomo Bank, one of your customers
would like a yen quote on Australian
dollars. Current market rates are:
Spot
30-day
¥101.37-85/U.S.$1
15-13
A$1.2924-44/U.S.$1
20-26
• a. What bid and ask yen cross rates
would you quote on spot Australian dollars?
• Answer. By means of triangular arbitrage,
we can calculate the market quotes for the
Australian dollar in terms of yen as
•
¥78.31-81/A$1
• b. What outright yen cross rates would
you quote on 30-day forward Australian
dollars?
Spot
30-day
30-day
outright
¥101.37-85/U.S.$1
15-13
¥101.22-72/U.S.$1
A$1.2924-44/U.S.$1
20-26
A$1.2944-70/U.S.$1
forward rates
• By means of triangular arbitrage, we can
then calculate the market quotes for the
30-day forward Australian dollar in terms
of yen as
•
¥78.04-58/A$1
• c. What is the forward premium or
discount on buying 30-day Australian
dollars against yen delivery?
Forward premium
or discount
=
Forward rate Spot rate
360
78.58 - 78.81 360
x
=
x
= - 3.43%
Forward contract
Spot rate
78.81
30
number of days
• 9. Suppose Air France receives the
following indirect quotes in New York:
€0.92 - 3 and £0.63 - 4. Given these
quotes, what range of £/ € bid and ask
quotes in Paris will permit arbitrage?
• Answer.
• Triangular arbitrage can take place in either of
two ways: (1) Convert from euros to dollars (at
the ask rate), then from dollars to pounds (at the
bid rate), or (2) convert from pounds to dollars
(at the ask rate), then from dollars to euros (at
the bid rate).
• The first quote will give us the bid price for the
euro in terms of the pound and the second quote
will yield the ask price. Using the given rates, Air
France would end up with the following amounts:
(1) Euros to pounds
(2) Pounds to euros
=
€/$ (ask)
x
$/£ (bid)
=
0.93
x
1/0.63
=
€ 1.4762/£ or £0.6774/ €
=
£/$ (ask)
x
$/ € (bid)
0.64
x
1/0.92
=
£0.6957/€ or €1.4375/£
• The import of the figures in method (1) is
that Air France can buy pounds in New
York for €1.4762/£, which is the equivalent
of selling euros at a rate of £0.6774/ €.
• So, if Air France can buy euros in Paris for
less than £0.6774/ € (which is the
equivalent of selling pounds for more than
€0.6774/£), it can earn an arbitrage profit.
• Similarly, the figures in method (2) tell us that Air
France can buy euros in New York at a cost of
£0.6957/ €. Given this exchange rate, Air France
can earn an arbitrage profit if it can sell these
euros for more than £0.6957/FF in Paris.
• Thus, Air France can profitably arbitrage
between New York and Paris if the bid rate for
the euro in Paris is greater than £0.6957/ € or
the ask rate is less than £0.6774/ €.
• 10.On checking the Telerate screen, you
see the following exchange rate and
interest rate quotes:
Currency
90-day interest rates annualized
Dollar
4.99% - 5.03%
Swiss franc
3.14% - 3.19%
Spot rates
90-day forward rates
$0.711 - 22
$0.726 - 32
• a. Can you find an arbitrage opportunity?
• Answer. Yes. There are two possibilities:
Borrow dollars and lend in Swiss francs or
borrow Swiss francs and lend in dollars.
The profitable arbitrage opportunity lies in
the former: Lend Swiss francs financed by
borrowing U.S. dollars.
• b. What steps must you take to capitalize
on it?
• Answer. Borrow dollars at 1.2575% for 90
days (5.03%/4), convert these dollars into
francs at the ask rate of $0.722, lend the
francs at 0.785% for 90 days (3.14%/4),
and immediately sell the francs forward for
dollars at the buy rate of $0.726.
• c. What is the profit per $1,000,000
arbitraged?
• Answer. The profit is $1,000,000 x
[(1.00785/0.722) x 0.726 - 1.012575] =
$858.66.