SUGGESTED SOLUTIONS TO CHAPTER 7 PROBLEMS

SUGGESTED SOLUTIONS TO CHAPTER 7 PROBLEMS 1. The $: E exchange rate is E1 = $0.95, and the E/SFr exchange rate is
SFr 1 = E0.71. What is the SFr/$ exchange rate? Answer. SFr1 = E0.71 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% In this case, the forward discounts at these maturities are relatively
small, indicating that Canadian and U.S. interest rates are close to each
other. 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? Answer. A premium of 66 points. b. What is the premium on 180-day euros? Answer. The 180-day premium is (0.9146 - 0.9080)/0.9080 x 2 = 1.45%. 5. Suppose Credit Suisse quotes spot and 90-day forward rates of $0.7957-
60, 8-13. a. What are the outright 90-day forward rates that Credit Suisse is
quoting? Answer. The outright forwards are: bid rate = $0.7965 (0.7957 + 0.0008) and
ask rate = $0.7973 (0.7960 + 0.0013). b. What is the forward discount or premium associated with buying 90-day
Swiss francs? Answer. The annualized forward premium = [(0.7973 - 0.7960)/0.7960]x 4 =
0.65%. c. Compute the percentage bid-ask spreads on spot and forward Swiss
francs. Answer. The bid-ask spread is calculated as follows: [pic]
Substituting in the numbers yields a spot bid-ask spread of (0.7960 -
0.7957)/0.7960 = 0.04%. The corresponding forward bid-ask spread is (0.7973
- 0.7965)/0.7973 = 0.10%. 6. Suppose Dow Chemical receives quotes of $0.009369-71 for the yen and
$0.03675-6 for the Taiwan dollar (NT$). a. How many U.S. dollars will Dow Chemical receive from the sale of ¥50
million? Answer. Dow must sell yen at the bid rate, meaning it will receive from
this sale $468,450 (50,000,000 x 0.009369). b. What is the U.S. dollar cost to Dow Chemical of buying ¥1 billion? Answer. Dow must buy at the ask rate, meaning it will cost Dow $9,371,000
(1,000,000,000 x 0.009371) to buy ¥1 billion. c. How many NT$ will Dow Chemical receive for U.S.$500,000? Answer. Dow must sell at the bid rate for U.S. dollars (which is the
reciprocal of the ask rate for NT$, or 1/0.03676), meaning it will receive
from this sale of U.S. dollars NT$13,601,741 (500,000/0.03676). d. How many yen will Dow Chemical receive for NT$200 million? Answer. To buy yen, Dow must first sell the NT$200 million for U.S. dollars
at the bid rate and then use these dollars to buy yen at the ask rate. The
net result from these transactions is ¥784,334,649.45 (200,000,000 x
0.03675/0.009371). e. What is the yen cost to Dow Chemical of buying NT$80 million? Answer. Dow must sell the yen for dollars at the bid rate and then buy NT$
at the ask rate with the U.S. dollars. The net yen cost to Dow from
carrying out these transactions is ¥313,886,220.51 (80,000,000 x
0.03676/0.009369) 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/E in London. Use the pounds to buy euros for
E1.6244/£ 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 These prices can be found as follows. For the yen bid price for the
Australian dollar, we need to first sell Australian dollars for U.S.
dollars and then sell the U.S. dollars for yen. It costs A$1.2944 to buy
U.S.$1. With U.S.$1 we can buy ¥101.37. Hence, A$1.2944 = ¥101.37, or A$1 =
¥78.31. This is the yen bid price for the Australian dollar. The yen ask price for the Australian dollar can be found by first selling
yen for U.S. dollars and then using the U.S. dollars to buy Australian
dollars. Given the quotes above, it costs ¥101.85 to buy U.S.$1, which can
be sold for A$1.2924. Hence, A$1.2924 = ¥101.85, or A$1 = ¥78.81. This is
the yen ask price for the Australian dollar. As a foreign exchange trader, you would try to buy Australian dollars at
slightly less than ¥78.31 and sell them at slightly more than ¥78.81.
Buying and selling Australian dollars at the market price will leave you
with no profit. How much better than the market prices you can do depends
on the degree of competition you face from other traders and the extent to
which your customers are willing to shop around to get better quotes. b. What outright yen cross rates would you quote on 30-day forward
Australian dollars? Answer. Given the swap rates, we can compute the outright forward direct
quotes for the yen and Australian dollar by adding or subtracting the
forward points as follows Spot 30-day 30-day outright
forward rates
¥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 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 These prices can be found as follows. For the yen bid price for the forward
Australian dollar, we need to first sell Australian dollars forward for
U.S. dollars and then sell the U.S. dollars forward for yen. It costs
A$1.2970 to buy U.S.$1 forward. With U.S.$1 we can buy ¥101.22. Hence,
A$1.2970 = ¥101.22, or A$1 = ¥78.04. This is the yen bid price for the
forward Australian dollar. The yen ask price for the Australian dollar can be found by first selling
yen forward for U.S. dollars and then using the U.S. dollars to buy forward
Australian dollars. Given the quotes above, it costs ¥101.72 to buy U.S.$1,
which can be sold for A$1.2944. Hence, A$1.2944 = ¥101.71, or A$1 = ¥78.58.
This is the yen ask price for the forward Australian dollar. c. What is the forward premium or discount on buying 30-day Australian
dollars against yen delivery? Answer. As shown in parts a and b, the ask rate for 30-day forward
Australian dollars is ¥78.58 and the spot ask rate is ¥78.81. Thus, the
Australian dollar is selling at a forward discount to the yen. The
annualized discount equals -3.43%, computed as follows: [pic] 9. Suppose Air France receives the following indirect quotes in New
York: E0.92 - 3 and £0.63 - 4. Given these quotes, what range of £/ E bid
and ask quotes in Paris will permit arbitrage? Answer. Triangular arbitrage can take place in either of two ways: (1)
Convert from euros to dollars (at the ask rate), then from dollars to
pounds (at the bid rate), or (2) convert from pounds to dollars (at the ask
rate), then from dollars to euros (at the bid rate). The first quote will
give us the bid price for the euro in terms of the pound and the second
quote will yield the ask price. Using the given rates, Air France would end
up with the following amounts: (1) Euros to pounds = E/$ (ask) x $/£ (bid)
= 0.93 x 1/0.63
= E 1.4762/£ or £0.6774/ E (2) Pounds to euros = £/$ (ask) x $/ E (bid)
0.64 x 1/0.92
= £0.6957/E or E1.4375/£ The import of the figures in method (1) is that Air France can buy pounds
in New York for E1.4762/£, which is the equivalent of selling euros at a
rate of £0.6774/ E. So, if Air France can buy euros in Paris for less than
£0.6774/ E (which is the equivalent of selling pounds for more than
E0.6774/£), 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/ E. 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