1. Using the following table, consider as American style call option on the euro. The
current euro spot exchange rate is $0.9657, and each option contract is for E62,500.
960
980
1000
1020
Calls
Vol.
...
14
1
1
Jun
Jun
Jun
Jun
Puts
Last
...
0.0188
0.0117
0.0600
Vol.
5
...
...
...
Last
0.0161
...
...
0.0100
a. Is the 980 call option currently in the money, at the money, or out of the
money?
ANSWER. The call option is currently out of the money.
b. Suppose that your corporate economist believes the euro may appreciate
against the dollar to an exchange value as high as $1.02 or depreciate to an
exchange value as low as $0.96. She therefore purchases eight call contracts to
partially hedge an underlying short exposure of 750,000 euros. Draw a diagram
illustrating the potential loss or gain on all eight contracts.
ANSWER. (0.0188)(62,500) = $1,175
($1,175)(8 contracts) = $9,400
Net Profit
10,600
0.960
0.980
1.02
0.9988
0
Break Even
9,400
Out of the Money
Net Loss
In the Money
At the Money
c. Indicate the amount of loss or profit at $0.96, $1.02 and the current spot rate.
(Keep all calculations to two decimal places).
ANSWER. $9,400, $.04(8*62,500) – 9,400 = $20,000 - $9,400 = $10,600. $9,400
d. Indicate the break-even rate.
ANSWER. .9988
e. Add to your diagram a line indicating the gain and loss on the underlying
exposure as the spot deviates from the current level. Indicate the gain or loss at
$0.96 and $1.02.
ANSWER. The intercepts are the spot rate (.9657) less .0141 [$10,600] and plus .0125 [$9,400], or
.9516 and .9782. At $.96 the gain would be $4,275 [750,000(.0057); at $1.02 the loss would be
$40,725.
ALTERNATIVE ANSWER. To determine Gain/Loss, find the euro value of short exposure at current
exchange rate and assume that for every exchange rate, the receiver of payment needs that many
euros.
Euro Obligation = $750000/0.9657 = 776,638.7077 euros
Gain/Loss = Short Exposure - (Euro Obligation)*(Exchange Rate)
Gain (exchange at .96)
= $750,000 – (776,638.7077)*(.96) = $4,426.84
Loss (exchange at 1.02) = $750,000 – (776,638.7077)*(1.02) = ($42,171.48)
(5 points)
2. Suppose a new nation decides to peg the value of its currency, the newbill, to a basket
consisting of 0.625 U.S. dollars and 0.25 British pounds. Further suppose the exchange
rate between the U.S. dollar and the British pound is 1.5 dollars per pound. If the basket
constitutes one newbill, what is the appropriate exchange value between the newbill and
the dollar, and between the newbill and the pound?
1 Newbill =
Exchange Rate $/£
Exchange Rate £/$
$ Value of £ portion of N
£ Value of $ portion of N
Exchange Rate N/£
Exchange Rate £/N
Exchange Rate N/$
Exchange Rate $/N
$0.6250
$1.5000
£0.6667
$0.3750
£0.4167
1.5000
£0.6667
1.0000
$1.0000
£0.2500
What is the weight assigned to the U.S. dollar in the currency basket? What is the weight
assigned to the British pound in the currency basket?
Weight $
Weight £
(3 points)
62.5%
37.5%
3. Why is a currency futures option a “derivative of a derivative”? (2points)
ANSWER. A currency future already is a derivative, because its value varies with the exchange
rate. The value of a currency futures option, in turn, depends on the underlying value of a currency
futures contract, so its value is derived from the futures derivative. In this way, a currency futures
option is a “derivative of a derivative.”
4. 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 [100ths of ¢/¥], while the price of the 1.01 put
is 1.6 [100ths of ¢/¥], what is the net cost of the bear spread?
ANSWER. Going long on the 103 March put costs the trader 0.0281¢/¥ while going short on the
101 March put yields the trader 0.016¢/¥. The net cost is therefore 0.0121¢/¥ (0.028 - 0.016). On a
contract of ¥6,250,000, this is equivalent to $756.25
b. What is the maximum amount the trader can make on the bear spread if 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 1.03¢/¥. Similarly, the 101 March put gives the buyer
the right but not the obligation to sell yen to the trader at a price of 1.01¢/¥. If the yen falls to
1.01¢/¥ or below, the trader will earn the maximum spread of 0.02¢/¥. After paying the cost of the
bear spread, the trader will net 0.079¢/¥ (0.02¢ - 0.0121¢), or $493.75 on a ¥6,250,000 contract.
c. Redo your answers to Parts a & b, assuming the trader executes a ‘bull spread’
consisting of a short PHLX 101 March call priced at 1.96 [100ths of ¢/¥] and a
long PHLX 99 March call priced at 3.91 [100ths of ¢/¥]. What is the trader’s
maximum profit? Maximum loss?
ANSWER. In this case, the trader will pay 0.0391¢/¥ for the long 99 March call and receive
0.0196¢/¥ for the short 101 March call. The net cost to the trader, therefore, is 0.0195¢/¥,
($1218.75) which is also the trader's maximum potential loss. At any price of 1.01¢/¥ or greater,
the trader will earn the maximum possible spread of 0.02¢/¥. After subtracting off the cost of the
bull spread, the trader will net 0.0005¢/¥, or $31.25 per ¥6,250,000 contract.
(5 points)
5. Suppose your company owes a 1,500,000 Australian dollar (A$) payment due in
November. If the A$ were to appreciate against the dollar, the dollar value of this future
payment will increase and your company will experience a loss. Because of this foreign
exchange risk exposure, you decide to use a futures contract as a hedge.
a. Explain how you would use A$ futures: number of contracts, long or short- and
how the futures account would act as a hedge.
ANSWER. To hedge a foreign exchange exposure, a customer assumes a position in the opposite
direction of the exposure. In this instance the company has more A$ liabilities than A$ assets.
That is: it is short A$. Hence, it must buy A$ to hedge its risk – or, go long. To fully hedge its risk
the company should buy 15 long contracts since A$ currency futures contracts are sold in lots of
A$ 100,000 therefore 15 x 100,000 = 1,500,000.
b. Suppose you undertake this transaction with December A$ futures on the first
of November at the moment the market opens. Show how your initial margin
changes daily (for the first through the fourth days). Indicate any cash flows
generated or margin calls.
1st
2nd
3trd
4th
Open
High
Low
Settle
Change
AUSTRALIAN DOLLAR (CME) – 100,000A$; $ per A$
November .5251
.5267
.5213
.5252
-.0046
November .5216
.5216
.5110
.5127
-.0125
November .5108
.5120
.5029
.5115
-.0012
November .5085
.5112
.5058
.5086
-.0029
Agreement
$
100,000
Change in account
st
1
2nd
3rd
4th
Interest
2,007
2,180
3,037
3,363
Maintenance
Initial
$ 1,100
$ 1,485
CF
Account end of day
$
10
$ 1,485
$ 1,495
$
(1,250)
$ 1,240
$ 1,485
$
(120)
$
0
$ 1,365
$
(290)
$
410
$ 1,485
c. How would you close out your position at the end of the fourth day?
ANSWER. We could close out this position at the end of the fourth day by either taking delivery of
the A$ 1,500,000 by paying 1,500,000*.5086 = $762,900 or we could close it out with an
offsetting trade.
(2 points)
6. In May 1988, Walt Disney Productions sold Japanese investors a 20-year stream of
projected yen royalties from Tokyo Disneyland. The present value of that stream of
royalties, discounted at 6% (the return required by the Japanese investors), was ¥93
billion. Disney took the yen proceeds from the sale, converted them to dollars, and
invested the dollars in bonds yielding 10%
a. At the time of the sale, the exchange rate was ¥ 124 = $1. What dollar amount
did Disney realize from the sale of its yen proceeds?
ANSWER. Disney realized 93,000,000,000/124 = $750,000,000 from the sale of its future yen
proceeds.
b. Demonstrate the equivalence between this transaction and a currency swap.
ANSWER. In a currency/interest rate swap, one party trades a stream of payments in one currency,
at one interest rate, for a stream of payments in a second currency, at a second interest rate.
Disney's stream of yen royalties can be treated as a yen bond, which it traded for a dollar bond,
with dollar payments. The only difference between the Disney swap and a traditional swap is that
the latter usually involve cash outflows whereas the Disney swap involves cash inflows.
c. Did Disney achieve the equivalent of a ‘free lunch’ through this transaction?
Explain.
ANSWER. Gary Wilson, Disney's chief financial officer, committed an unpardonable analytical
sin when he claimed that: "In effect, we got money at a 6% discount rate, reinvested it at 10%,
and hedged our royalty stream against yen fluctuations -- all in one transaction." He was
comparing apples with oranges: in this case, a 6% yen interest rate with a 10% dollar interest
rate. The international Fisher effect tells us that the most likely reason that the yen interest rate is
4 percentage points less than the equivalent dollar interest rate is because the market expects the
dollar to depreciate by about 4% annually against the yen, although as it happens the exchange
rate is currently ¥ 124 = $1. Corporate bond rates on AAA-rated, eight-year maturities are about
6 percent in US and 2 percent in Japan.
(3 points)