======================CHAPTER 7==============================
SUGGESTED ANSWERS TO CHAPTER 7 QUESTIONS
1. Answer the following questions based on data in Exhibit 7.4.
a. How many Swiss francs can you get for one dollar?
ANSWER. The indirect quote is $1 = SFr 1.6545.
How many dollars can you get for one Swiss franc?
ANSWER. The direct quote is SFrl = $0.6044.
c. What is the three-month forward rate for the Swiss franc?
ANSWER. The three-month forward rate is SFrI = $0.6044.
Is the Swiss franc selling at a forward premium or discount?
ANSWER. For the one-month and three-month forward Swiss franc the answer
is neither since the forward rate equals the spot rate. The 6-month Swiss
franc is selling at a premium
since the forward rate exceeds the spot rate.
e. What is the 90-day forward discount or premium on the Swiss franc?
ANSWER. The 90-day forward premium is 0.
2. What risks confront dealers in the foreign exchange market? How
can they cope with these risks?
ANSWER. Foreign exchange dealers must cope with exchange risk, because
of the foreign currency positions they take. They also bear credit risks
since the counterparties to the trades
they enter into may not honor their obligations.
They can cope with currency risk by using forward contracts and currency
options (see Chapter 10), widening ask quotes, and limiting the position
they are willing to take in any one
currency. They can limit credit risk by the position they are willing
to take with any one customer and by setting margin requirements that vary
with the riskiness of their customers (banks
will generally not do this).
3. Suppose a currency increases in volatility. What is likely to happen
to its bid-ask spread? Why?
ANSWER. As a currency’s volatility increases, it becomes riskier for
traders to take positions in that cur compensate for the added risks, traders
quote wider bid-ask spreads.
4. Who are the principal users of the forward market? What are their
motives?
ANSWER. The principal users of the forward market are currency arbitrageurs,
hedgers, importers and expo speculators. Arbitrageurs wish to earn risk-free
profits; hedgers, importers
and exporters want to protect the home currency values of various foreign
currency-denominated assets and liabilities; and speculators actively themselves
to exchange risk to benefit
from expected movements in exchange rates.
5. How does a company pay for the foreign exchange services of a commercial
bank?
ANSWER. Companies compensate banks for foreign exchange services through
the bid-ask spread. The bank foreign exchange at the bid rate (low) and
sell at the ask rate (high).
SUGGESTED SOLUTIONS TO CHAPTER 7 PROBLEMS
1. ANSWER. SFrl = €0.71 x 0.95 = $0.6745.
2. ANSWER. The direct quote for the dollar in London is just the reciprocal
of the direct quote for the pound in N
or 1/1.1115 - 1/1.1110 = 0.8997-0.9001
3. Using the data in Exhibit 7.4, calculate the 30-day, 90-day, and
180-day forward discounts for the Canadian
ANSWER. Here are the relevant rates for the Canadian dollar:
Spot;
C$1 = $0.6342
30-day forward:
C$1 = $0.6340
90-day forward:
C$l = $0.6338
180-day forward: C$l
= $0.6338
The 30-day forward discount is: [($0.6340-$0.6342)/$0.6342] x 12 =
0.38%
The 90-day forward discount is: [($0.6338 - $0.6342)/$0.6342] x 4 =
0.25%
The 180-day forward discount is: [($0.6338 - $0.6342)/$0.6342] x 2
= 0.13%
In this case, the forward discounts at these maturities are very small,
indicating that Canadian and U.S. interest rates are virtually identical.
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 premium on 180-day euros?
ANSWER. The 180-day premium is (0.9146 - 0.9080)10.9080 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.
Substituting in the numbers yields a spot bid-ask spread of (0.7960
- 0.7957) = 0.04%. The corresponding forward bid-ask spread is (0.7973
- 0.7965) = 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
V50 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
yen?
ANSWER. Dow must buy at the ask rate, meaning it will cost Dow $9,371,000
(1,000,000,000 x 0.009371) to buy 1 billion yen.
c. How many NT$ 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 1/0.0367 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 the dollars to buy yen at the ask
rate. The net result from these transactions is
784,334,649.45 (200,000,000 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. Tb net yen cost to Dow from
carrying out these transactions is
1313,886,220.51(80,000,000 x 0.03676/0.009369)
7. Suppose the euro is quoted at 0.6064-80 in London, and the pound
sterling is quoted at 1.6244-59 in Frankfurt.
a. Is there a profitable arbitrage situation? Describe it.
ANSWER. Buy euros for £0.6080. Use the euros to buy pounds for
€1 .6259. This is equivalent to selling euros lot £0.6150. There
is a net profit of £00070 per euro bought and
sold—a percentage yield of 1.16% (0.0070/0.6080).
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) = 0.09%
euro bid-ask spread = (0.6080 - 0.6064)/0.6080=0.26%
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:
30-day
1101 .37-85/U.S.$l 15-13
A$l.2924-44/LJ.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 ol yen as
178.3l-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 yen 101.37. Hence, A$1.2944
=Y101.37, orA$1 =Y78.31 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 Y10l
.85 to buy U.S.$1, which can be sold for A$1.2924. Hence, A$1.2924
= k or Mi = V78.81. This is the yen askprice for the Australian dollar.
As a foreign exchange trader, you would try to buy Australian dollars
at slightly less than V78.3 1 and sell them at slightly more than V78.8
I. 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 forwani direct
quotes for the yen and Australian dollar by adding or subtracting the forward
points as follows
flgj 30-day 30-day outright
forward rates
V1O1.37-85/U.S.$1 15-13 Vl01.22-721U.S.$l
A$1.2924-44/U.S.$1 20-26 A$1.2944-70
By means of triangular arbitrage, we can then calculate the market
quotes for the 30-day forward Australian dollar in terms of yen as
V78.04-58
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$1.2970 to buy
U.S.$l forward. With IJ.S.$I we can buy V101.22. Hence, A$1.2970 =VIOI.22,
orA$1 =V78.04. This is the yen bid
price for the forward Australian dollar.
The yen ask price for the Australian dollar can he 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 V101.72 to buy U.S.$1, which can be sold for A$1 .2944.
Hence, A$I .2944 = VIOl .71, or A$l V78.58. 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 V78.58 and the spot ask rate is V78.81. Thus, the
Australian dollar is selling at a forward
discount to the yen. The annualized discount equals -3.43%, computed
as follows:
Forward premium = Forward rate - Spot rate 360
= 78.58 - 78 =
or discount Spot rate
Forward contract
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 £I€ 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
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
Y101.85 to buy U.S.$1, which can be sold for A$1.2924. Hence, A$1.2924
=Y101.85, or A$l = 178.81. 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 Y78.31 and sell them at slightly more than Y78.81.
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
30-day 30-day outright forward rates
Y101 .37-85/U.S.$l 15-13 Y101.22-72/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
178.04-58/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$1 .2970 to buy U.S.$l forward. With U.S.$1
we can buy 1101.22. Hence, A$1.2970 =1101.22, or A$1 =178.04. 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 Y101.72 to buy U.S.$1, which can be sold for A$1.2944.
Hence, A$1.2944 =Y101.71, or A$1 =Y78.58. 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 Y78.58 and the spot ask rate is Y78.81. Thus, the
Australian dollar is selling at a forward
discount to the yen. The annualized discount equals -3.43%,
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 £I€ 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 s quote will yield the ask
price. Using the given rates, Air France would end up with the following
amounts:
(1) Euros to pounds
€ 1.4762/12 or £0.6774/€
(2) Pounds to euros
£0.6957/€ or €14375112
The import of the figures in method (1) is that Air France can buy
pounds in New York for € 1.4762/Pound, which equivalent of selling
euros at a rate of £0.67741/€. 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/Pound), it can earn an arbitrage
profit. Similarly, the figu 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 Franc4ci profitably arbitrage
between New York and Paris if the bid rate for the euro in Paris is greater
than £0.69571€ or ask rate is less than
£0.6774/€.
10. On checking the Telerate screen, you see the following exchange
rate and interest rate quotes:
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 L in dollars. The profitable arbitrage
opportunity lies in the former: Lend
Swiss francs financed by borrowing U.S. do!
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 $0.72 lend the francs at 0.785%
for 90 days (3. 14%/4), and
immediately sell the francs forward for dollars at the buy rate
$0726.
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.
======================CHAPTER 8==============================
SUGGESTED ANSWERS TO CHAPTER 8 QUESTIONS
1. On April 1, the spot price of the British pound was $1.86 and the
price of the June futures contract was $1.85. During April the pound appreciated,
so that by May lit was selling for
$1.91. What do you think happened to the price of the June pound futures
contract during April? Explain.
ANSWER. The price of the June futures contract undoubtedly rose. Here’s
why. The June futures price is based on the expectations of market participants
as to what the spot value of
the pound will be at the date of settlement in June. Since the spot
value of the pound has risen in during April, the best prediction is that
the future level of the pound will also be higher
than it was on April 1. This expectation will be undoubtedly be reflected
in a June pound futures price that is higher on May 1 than it was on April
1.
2. What are the basic differences between forward and futures contracts?
Between futures and options contracts?
ANSWER. The basic differences between forward and futures contracts
are described in Section 3.1. The most important difference between these
two contracts and an options
contract is that a buyer of a forward or futures contract must take
delivery, while the buyer of an options contract has the right but not
the obligation to complete the contract.
3. A forward market already existed, so why it was necessary to establish
currency futures and currency options contracts?
ANSWER. A currency futures market arose because private individuals
were unable to avail themselves of the forward market. Currency options
are partly a response to individuals and
firms who would like to eliminate some currency risk while at the same
time preserving the possibility of earning a windfall profit from favorable
movements in the exchange rate. Options
also enable firms bidding on foreign projects to lock in the home currency
value of their bid without exposing themselves to currency risk if their
bid is rejected.
4. Suppose that Texas Instruments must pay a French supplier €10
million in 90 days.
a. Explain how TI can use currency futures to hedge its exchange risk.
How many futures contracts will TI need to fully protect itself?
ANSWER. TI can hedge its exchange risk by buying euro futures contracts
whose expiration date is the closest to the date on which it must pay its
French supplier. Given a contract size
of €125,000, TI must buy 10,000,000/125,000 = 80 futures contracts
to hedge its euro payable.
b. Explain how TI can use currency options to hedge its exchange risk.
How many options contracts will TI need to fully protect itself?
ANSWER. TI can hedge its exchange risk by buying euro call options
contracts whose expiration date is the c to the date on which it must pay
its French supplier. Given a contract size
of €62,500, TI must buy 10,000,0.00/62,500
= 160 options contracts to hedge its payable.
c. Discuss the advantages and disadvantages of using currency futures
versus currency options to hedge ‘IT exchanges risk.
ANSWER. A futures contract is most valuable when the quantity of foreign
currency being hedged is known, as i the case here. An option contract
is most valuable when the quantity of
foreign currency is unknown. Other thin being equal, therefore, TI
should use futures contracts to hedge its currency risk. However, TI must
honor its future contracts even if the spot rate
at settlement is less than the futures price. In contrast, TI can choose
not to exercise currency call options if the call price exceeds the spot
price. Although this feature is an advantage of
currency options, it is fully priced out in the market via the call
premium. Hence, options are not unambiguously better than futures. In this
case, since the quantity of the future French
franc outflow is known, TI should use currency futures to hedge its
risk.
5. Suppose that Bechtel Group wants to hedge a bid on a Japanese construction
project. But because the yen exposure is contingent on acceptance of its
bid, Bechtel decides to buy a
put option for the V15 billion bid amounts rather than sell it forward.
In order to reduce its hedging cost, however, Bechtel simultaneously sells
a call option for V15 billion with the same
strike price. Bechtel reasons that it wants to protect its downside
risk on the contract and is willing to sacrifice the upside potential in
order to collect the call premium. Comment on
Bechtel’s hedging strategy.
ANSWER. The combination of buying a put option and selling a call option
at the same strike price is equivalent to selling Vl5 billion forward at
a forward rate equal to the strike price on
the put and call options. That is, Bechtel is no I longer holding an
option; it is now holding a forward contract. If the yen appreciates and
Bechtel loses its bid, it will face an exchange loss
equal to 15 billion x (actual spot rate - exercise price).
PROBLEMS
1.Net profit is $1,250 - 937.50 = $312.50.
2. Suppose that the forward ask price for March 20 on euros is $0.91
27 at the same time that the price of 1MM euro futures for delivery on
March 20 is $0.9 145. How could an
arbitrageur profit from this situation? What will be the arbitrageur’s
profit per futures contract (size is €125,000)?
ANSWER. Since the futures price exceeds the forward rate, the arbitrageur
should sell futures contracts at $0.9145 and buy euro forward in the same
amount at $0.9127. The
arbitrageur will earn 125,000(0.9145 .0.9127) = $225 per euro futures
contract arbitraged.
3. Suppose that DEC buys a Swiss franc futures contract (contract size
is SFr 125,000) at a price of $0.83. If the spot rate for the Swiss franc
at the date of settlement is SFr 1 =
$0. 8250, what is DEC gain or loss on this contract?
ANSWER. DEC has bought Swiss francs worth $0.8250 at a price of $0.83.
Thus, it has lost $0.005 per franc for a total toss of 125,000 x .005 =
$625.
4. On January 10, Volkswagen agrees to import auto parts worth $7 million
from the United States. The parts will be delivered on March 4 and are
payable immediately in dollars. VW
decides to hedge its dollar position by entering into 1MM futures contracts.
The spot rate is $0.8947/€ and the March futures price is $0.9002/€.
a. Calculate the number of futures contracts that VW must buy to offset
its dollar exchange risk on the parts contract.
ANSWER. Volkswagen can lock in a euro price for its imported parts
by buying dollars in the futures market at the current March futures price
of €1.1109/$1 (1/0.9002). This is
equivalent to selling euro futures contracts. At that futures price,
VW will sell €7,776,050 for $7 million. At €125,000 per futures
contract, this would entail selling 62 contracts
(7,776,050/125,000 = 62.21) at a total cost of €7,750,000.
b. On March 4, the spot rate turns out to be $0.8952/€, while
the March futures price is $0.8968/€. Calculate VW’s net euro gain
or loss on its futures position. Compare this figure with
VW’s gain or loss on its unhedged position.
ANSWER. Under its futures contract, Volkswagen has agreed to sell €7,750,000
and receive $6,976,550 (7,750,000 x 0.9002). On March 4, VW can close out
its futures position by
buying back 62 March euro futures contracts (worth €7,750,000).
At the current futures rate of $0.8968/€, VW must pay out $6,950,200
(7,750,000 x 0.8968). Hence, VW has a net
gain of $26,350 ($6,976,550 -$6,950,200) on its futures contract. At
the current spot rate of $0.8952/€, this translates into a gain of
€29,434.76 (26,350/0.8952). Upon closing out the
62 futures contracts, VW will then buy $7 million in the spot market
at a spot rate of $0.8952/€. Its net cost is €7,790,046.92 (7,000,000/0.8952
- 29,434.76).
If VW had not hedged its import contract, it could have bought the
$7 million on March 10 at a cost of €7,819,481.68 (7,000 ,000/0 .8952).
This contrasts with a projected cost based
on the spot rate on January 10th of €7,823,851.57 (7,000,000/0.8947).
However, the latter “cost” is irrelevant since VW had no opportunity to
buy March dollars at the January 10th
spot rate of $0.8947/€. By not hedging, VW would have paid an
extra €29,434.76 for the $7,000,000 to satisfy its dollar liability,
the difference between the cost of $7 million with
hedging (€ 7,790,046.92) and the cost without hedging (€7,819,481.68).
5. Citigroup sells a call option on euros (contract size is €500,000)
at a premium of $0.04 per euro. If the exercise price is $0.91 and the
spot price of the euro at date of expiration is
$0.93, what is Citigroup’s profit (loss) on the call option?
ANSWER. Since the spot price of $0.93 exceeds the exercise price of
$0.91, Citigroup’s counterparty will exercise its call option, causing
Citigroup to lose 20 per euro. Adding in the
40 call premium it received gives Citigroup a net profit of 20 per
euro on the call option for a total gain of .02 x 500,000 = $10,000.
6. Suppose you buy three June PHLX call options with a 90 strike price
at a price of 2.3 (oI€).
a. What would be your total dollar cost for these calls, ignoring broker
fees?
ANSWER. With each call option being for €62,500, the three contracts
combined are for €187,500. At a price of 2.3 the total cost is therefore
187,500 x $0023 = $4,312.50.
b. After holding these calls for 60 days, you sell them for 3.8 ($/€).
What is your net profit on the contracts assuming that brokerage fees on
both entry and exit were $5 per contract and
that your opportunity cost was 8% per annum on the money tied up in
the premium?
ANSWER. The net profit would be 1 .5c/euro (3.8-2.3) for a total profit
before expenses of $2,812.50 (0.015 x 187,500).
Brokerage fees totaled $10 per contract or $30 overall. The opportunity
cost would be $4,312.50 x 0.08 x 60/365 = $56.71. After deducting these
expenses (which total $86.71), the
net profit is $2,725.79.
7. A trader executes a “bear spread” on the Japanese yen consisting
of a long PHLX 103 March put and a short PHLX 101 March put.
a. If the price of the 103 put is 2.81 (l00ths of c/Y), while the price
of the 101 put is 1.6 (l00ths of C/Y), what is the net cost of the bear
spread?
ANSWER. Going long on the 103 March put costs the trader 0.0281 c/y
while going short on the 101 March put yields the trader 0.016c/Y. The
net cost is therefore 0.0121c/Y
(0.028- 0.016). On a contract of Y6,250,000, this is equivalent to
$756.25.
b. What is the maximum amount the trader can make on the bear spread
in the event the yen depreciates against the dollar?
ANSWER. To begin, it should be pointed out that the 103 March put gives
the trader the right but not the obligation to sell yen at a price of 1
.03C/y. Similarly, the 101 March put gives
the buyer the right but not the obligation to sell yen to the trader
at a price of 1.01c/y. If the yen falls to 1.01c/y or below, the trader
will earn the maximum spread of 0.02c/y. After
paying the cost of the bear spread, the trader will net 0.079c/y (0.02
- 00121$), or $493.75 on a Y6,250,000 contract.
c. Redo your answers to parts a and b assuming the trader executes
a “bull spread” consisting of a long PFILX 97 March call priced at 0.03210/V
and a short PHLX 103 March call
priced at 0.01960/V. What is the trader’s maximum profit? Maximum loss?
ANSWER. In this case, the trader will pay 0.0321c/y for the long 97
March call and receive 0.0196c/y for the short 103 March call. The net
cost to the trader, therefore, is 0.0125c/Y,
which is also the trader’s maximum potential loss.At any price of 1.03c/y
or greater, the trader will earn the maximum possible spread of 0.06c/y.
After subtracting off the cost of the bull
spread, the trader will net 0.0475c/y, or $2,968.75 per Y6,250,000
contract.
8. b. Calculate what Apex would gain or lose on the option and futures
positions if the yen settled at its most likely value.
ANSWER. If the yen settles at its most likely price of $0007900, Apex
will not exercise its call option and will lose the call premium of $18,750.
If Apex hedges with futures, it will have
to buy yen at a price of $0.007940 when the spot rate is $0.0079. This
will cost Apex $0000040/V. for a total futures contract cost of 0.000040
x 125,000,000 = $5,000.
c. What is Apex’s break-even future spot price on the option contract?
On the futures contract?
ANSWER. On the option contract, the spot rate will have to rise to
the exercise price plus the call premium for Apex to break even on the
contract, or $0.008000 + $0.000150 =
$0.008 150. In the case of the futures contract, break-even occurs
when the spot rate equals the futures rate, or $0.007940.
d. Calculate and diagram the corresponding profit and loss and break-even
positions on the futures and options contracts for the sellers of these
contracts.
ANSWER. The sellers’ profit and loss and break-even positions on the
futures and options contracts will be the mirror image of Apex’s position
on these contracts. For example, the
sellers of the futures contract will breakeven at a future spot price
of Vi = $0.007940, while the options sellers will breakeven at a future
spot rate of Vi = $0.008 150. Similarly, if the
yen settles at its minimum value, the options sellers will earn the
call premium of $18,750 and the futures sellers will earn $55,000. But
if the yen settles at its maximum value of
$0.008400, the options sellers will lose $31,250 and the futures sellers
will lose $57,500.
==============CHAPTER 15======================================
SUGGESTED ANSWERS TO CHAPTER 15 QUESTIONS
l.As seen in Exhibit 15.2, Hong Kong stocks are over twice as volatile
as U.S. stocks. Does that mean that risk-averse American investors should
avoid Hong Kong equities? Explain.
ANSWER. No. Although Hong Stock stocks are much more volatile /than
U.S. stocks, their systematic component of risk is relatively low because
of the low correlation with the U.S.
market. The net result is that the systematic risk (beta) of the average
Hong Kong stock from a U.S. perspective is only 0.85, compared with a beta
of 1.0 for the average U.S. stock. In
other words, diversifying into Hong Kong stocks will reduce the riskiness
of a portfolio currently concentrated in U.S. stocks.
2. What characteristics of foreign securities lead to diversification
benefits for American investors?
ANSWER. The two basic characteristics are:
a)Many foreign securities are issued by companies that produce goods
and services not available from U.S. companies.
b)All U.S. companies are more or less subject to the same cyclical
economic fluctuations. Foreign securities by contrast involve claims on
economies whose cycles are not perfectly in
phase with the U.S. economic cycle. Thus, just as movements in different
stocks partially offset one another in an all-U.S. portfolio, so also movements
in U.S. and non-U.S. stocks
cancel out each other somewhat.
3. Will increasing integration of national capital markets reduce the
benefits of international diversifications?
ANSWER. Despite increasing integration of national capital markets,
they still don’t march in lock step. Some economies and, hence, their markets
will do befter than others at any given
time, so having stakes in several countries still spreads risks. Nonetheless,
increasing integration could lead to more comovement in common risk factors
(e.g., real interest rate changes).
If so, this will increase the correlation of national markets and decrease
the risk-reducing benefits of diversifying internationally. Ultimately,
it’s an empirical issue, and one that should be
ANSWER. Domestic stocks are more highly correlated because they are
all subject in one way or another to the state of the domestic economy.
The lower correlations between
domestic and foreign stocks reflect the lower correlations between
the domestic and foreign economies. These lower correlations also imply
that international investing is likely to lead to
greater diversification than just investing across industries within
a country. As the text shows, these lower correlations appear to be persisting
despite the greater integration of the global
economy.
5. Who is likely to gain more from investing overseas, a resident of
the United States or of Mexico? Explain.
ANSWER. Mexican investors will gain much more from international investing.
The size of the U.S. economy is such that the U.S. and world stock markets
are highly correlated whereas
the Mexican stock market, being much smaller, shows a much lower correlation
with the world stock market. The result is greater diversification (and,
I hence, risk reduction) benefits for
the Mexican investor than for the U.S. investor. In addition, the U.S.
has a much greater range of industries than does Mexico, giving much more
scope for industry diversification outside
Mexico than would be true for a U.S. investor who has access to such
a broad range of industries already.
6-Suppose that Mexican bonds are yielding more than 100% annually.
Does this high yield make them suitable for American investors looking
to raise the return on their portfolios?
Explain.
ANSWER. These returns are denominated in nominal peso terms, subjecting
them to currency risk. Nonetheless, holding a small percentage of your
portfolio in Mexican bonds will
reduce its risk, without sacrificing expected return. This is because
arbitrage will equilibrate expected returns across countries at the same
time that the actual returns from the Mexican
peso bonds are relatively uncorrelated with returns on the U.S. stock
market. Hence, the primary reason for holding Mexican bonds is to reduce
risk, not raise expected return.
7. According to one investment advisor, UJ feel more comfortable investing
in Western Europe or Canada. I would not invest in South America or other
regions with a record of debt
defaults and restructuring. The underwriters of large new issues of
ADRs of companies from these areas assure us that things are different
now. Maybe, but who can say that a
government that has defaulted on debt won’t change the rules again?”
Comment on this statement.
ANSWER, it’s true. A nation that has already defaulted on its debt
is less trustworthy than one that never has. However, this possibility
has already been factored into the prices of that
nation’s bonds and stocks in the form of a large discount to what they
would sell for absent that past experience. The real--and important--question
is whether the discount is high enough
to provide an expected return high enough to compensate for those risks.
If so, then Latin American stocks and bonds would be a reasonable investment
since they would provide
additional A diversification benefits.
8-Investors should avoid Hong Kong, given its problematic outlook now
that Britain has surrendered the colony to China. Comment.
ANSWER. The problematic outlook for Hong Kong now that it is a special
province of China is already reflected in the price of Hong Kong assets
(in the form of discounted prices).
Thus, the expected risk-adjusted return on Hong Kong assets is the
same as that on assets elsewhere. It is precisely these different risks,
which are uncoordinated with risks elsewhere
that give rise to the benefits of international diversification.
ANSWER. Note that the same argument could be made as to why non Japanese
investors should also invest all their money in Japan. Implicit in this
argument is the expectation that
historically high returns will persist into the future. Such an expectation
is an unreasonable one in efficient markets. Thus, unless one unrealistically
expects these superior returns to persist
into the future, diversification would make sense for both Japanese
and non Japanese investors. The benefits of this diversification were pointed
out in 1990, when the Tokyo Stock
Exchange fell 35% in dollar terms (39% in yen), while the Morgan Stanley
Capital International World Index fell by “just” 18.6% in dollar terms.
b. What arguments would you use to persuade a Japanese investor to
invest overseas?
ANSWER. Here are two arguments. First, you can’t expect stock markets
to keep going up in a straight line. All markets entail risk, and one way
to counter that risk is through
diversification. This argument should by now be bolstered by the crash
of the Japanese stock market in 1990. Second, to the extent that the Japanese
investor consumes foreign goods
and services, international investing can reduce the risk associated
with the investor’s consumption stream by matching foreign currency inflows
with foreign currency outflows. For
example, if the yen depreciates, the higher yen cost of buying foreign
goods and services will be offset by the higher yen value of foreign assets.
c. Why might Japanese (and other) investors still prefer to invest
in domestic securities despite the potential gains from international diversification?
ANSWER. If investors buy mostly domestic goods and services (or at
least goods and services priced in a domestic context), investing overseas
will expose them to currency risk that is
not offset by gains on the consumption side. For example, if the yen
appreciates, the yen value of dollar assets will decline. If the Japanese
investor is not consuming much in the way of
U.S. goods and services, the reduction in consumption costs will not
offset the investment losses.
10. Because ADRs are denominated in dollars and are traded in the United
States, they present less foreign exchange risk to U.S. investors than
do the underlying foreign shares of stock.
Comment.
ANSWER. ‘the answer to this question depends on the distinction between
the currency of denomination and the currency of determination. Although
the ADR currency of denomination
is the dollar, the currency of determination is the local currency
(or whatever currency determines the cash flows of the stock). More specifically,
the price of an ADR is the price of the
share of stock in its foreign currency multiplied by the spot dollar
value of the foreign currency. As the spot exchange rate changes, the dollar
price of the ADR will also change (unless the
foreign currency value of the stock changes in inverse proportion to
the change in the spot price, an unlikely scenario). Hence, ADRs are as
subject to exchange risk as the underlying
shares of foreign stock.
SUGGESTED SOLUTIONS TO CHAPTER 15 PROBLEMS
1. ANSWER. 3.79%
2. The dollar return on Swiss bonds equaled (1 - .016)(1 + 0.08) -
1 = 6.27%. The return on French bonds was lower at (1.018)(1.026) - 1 =
4.45%. In this case, Swiss franc
appreciation more than offset the lower local currency return on Swiss
bonds.
3.Substituting in the numbers yields a total dollar return on Toyota
stock for the year of 51.17%:
Note that yen appreciation during the year was (145 - 120) = 20.83%.
4. During 1989, the Mexican stock market climbed 112% in peso terms
while the peso depreciated by 28.6% against the U.S. dollar. What was the
dollar return on the Mexican stock
market during the year?
ANSWER. According to these data, the dollar return on the Mexican stock
market during 1989 was 51.37%:
it = (1 ÷ 1.12)0 - 0.286) - I = 51.37%
5a. in 1992, the Brazilian market rose by 1,117% in cruzeiro terms,
while the cruzeiro fell by 91.4% in dollar terms. Meanwhile, the U.S. market
rose by 8 which market did better?
ANSWER. The dollar return on the Brazilian market can be calculated
as 4.66%
The numbers reflect the fact that a return of 1,127% is equivalent
to receiving an additional Cr11.17 for each Cr1 invested. Based on these
figures, the U.S. market return of 8.5% bested
the dollar return on the Brazilian market by almost 4 percentage points.
b. In 1993, the Brazilian market rose by 4,190% in cruzeiro terms,
while the cruzeiro fell by 95.9% in dollar terms. Did the Brazilian market
do better in dollar temis in 1992 or in 1993?
ANSWER. Redoing the numbers in the answer to part a, we see that the
Brazilian market did far better in 1993 than in 1992:
= (1 + 41.90)0 - 0.959) - 1 = 75.89%
In this case, the extraordinarily large local currency return more
than offset the dramatic devaluation of the cruzeiro.
6. Suppose that the dollar is now worth _l.1372. If one-year German
bunds are yielding 9.8% and one-year U.S. Treasury bonds are yielding 6.5%,
at what end-of-year exchange rate
will the dollar returns on the two bonds be equal? What amount of euro
appreciation or depreciation does this equilibrating exchange rate represent?
ANSWER. To begin, given that German bunds are yielding more than U.S.
Treasuries, it is clear that for dollar returns on these two securities
to equilibrate, the euro must depreciate
against the dollar by about the interest differential, which is 3.3%.
Using Equation 15.4, the expected dollar return on investing $1 in a bund
(after first converting it into _1.1372) for a
year can be found as
1.l372(l.098)e1 = 1.2486e1 where e is the unknown end-of-year exchange
rate ($/J. Note that ex ante, one cannot anticipate any capital gains or
losses on investing. Setting this figure
equal to the $1 .065 expected dollar return from investing one dollar
in a Treasury bond yields the solution e = $0.8529, which converts into
a direct quote for the dollar of _1.1724. This
exchange rate entails a euro depreciation of (1.1372 - 1.1724)/1.1724
= -3.01% against the dollar. Alternatively, the dollar has appreciated
against the euro by (1.1724 - 1 = 3.10%.
7. In 1990, Matsushita bought MCA Inc. for $6.1 billion. At the time
of the purchase, the exchange rate was about Y1451$. By the time that Matsushita
sold an 80% stake in MCA to
Seagram for $5.7 billion in 1995, the yen had appreciated to a rate
of about Y971$.
a. Ignoring the time value of money, what was Matsushita’s dollar gain
or loss on its investment in MCA?
ANSWER. If an 80% stake in MCA was worth $5.7 billion, then the entire
firm was worth $7.125 billion. Based on this valuation, Matsushita actually
made $1 .025 billion on its
purchase of MCA. That is, by buying MCA at a price of $6.1 billion
and selling it for a price that valued the business at $7. 125 billion,
Matsushita made $1 .025 billion.
b. What was Matsushita’s yen gain or loss on the sale?
ANSWER. Taking into account the differences in exchange rates, Matshushita
paid Y884,500,000,000 (6,100,000,000 x 145) for MCA in 1990 and sold MCA
in 1995 for a price
that valued it at Y691,125,000,000 (7,125,000,000 x 97). The net result
was a loss for Matsushita of Y193,375,000,000 on its purchase of
MCA.
c. What did Matsushita’s yen gain or loss translate into in terms of
dollars? What accounts for the difference between this figure and your
answer to part a?
ANSWER. Matsushita’s yen loss converts into a dollar loss of $1,993,556,701
(193,375,000,000/97). This figure differs from the answer in part a because
it takes into account the
change in exchange rates between 1990 and 1995. In effect, it asks
what would have happened if Matsushita had held onto its yen instead of
converting them into a dollar asset that
didn’t appreciate in line with the yen’s appreciation. In other words,
this computed dollar loss represents an opportunity cost