Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
8. Suppose that you are a U.S.-based importer of goods from the United Kingdom. You expect
the value of the pound to increase against the U.S. dollar over the next 30 days. You will be
making payment on a shipment of imported goods in 30 days and want to hedge your currency
exposure. The U.S. risk-free rate is 5.5 percent, and the U.K. risk-free rate is 4.5 percent. These
rates are expected to remain unchanged over the next month. The current spot rate is $1.50.
a. Indicate whether you should use a long or short forward contract to hedge currency risk.
b. Calculate the no-arbitrage price at which you could enter into a forward contract that expires
in three months.
c. Move forward 10 days. The spot rate is $1.53. Interest rates are unchanged. Calculate the
value of your forward position.
d. Using the text software spreadsheet TRANSEXP, replicate the analysis in Exhibit 8.8.
Solution:
a. The risk to you is that the value of the British pound will rise over the next 30 days and it will
b. S0 = $1.50
T = 30/365
MINICASE: AIRBUS’ DOLLAR EXPOSURE
Airbus sold an aircraft, A400, to Delta Airlines, a U.S. company, and billed $30 million payable in
six months. Airbus is concerned with the euro proceeds from international sales and would like
to control exchange risk. The current spot exchange rate is $1.05/€ and six-month forward
exchange rate is $1.10/€ at the moment. Airbus can buy a six-month put option on U.S. dollars
with a strike price of €0.95/$ for a premium of €0.02 per U.S. dollar. Currently, six-month interest
rate is 2.5% in the euro zone and 3.0% in the U.S.
a. Compute the guaranteed euro proceeds from the American sale if Airbus decides to hedge
using a forward contract.
b. If Airbus decides to hedge using money market instruments, what action does Airbus need to
take? What would be the guaranteed euro proceeds from the American sale in this case?
c. If Airbus decides to hedge using put options on U.S. dollars, what would be the ‘expected’
euro proceeds from the American sale? Assume that Airbus regards the current forward
exchange rate as an unbiased predictor of the future spot exchange rate.
d. At what future spot exchange rate do you think Airbus will be indifferent between the option
and money market hedge?
Solution:
b. Airbus will borrow the present value of the dollar receivable, i.e., $29,126,214 =
c. Since the expected future spot rate is less than the strike price of the put option, i.e.,
€0.9091< €0.95, Airbus expects to exercise the put option on $ and receive €28,500,000 =
d. At the indifferent future spot rate, the following will hold:
€28,432,732 = ST (30,000,000) - €615,000.
Case Application: Richard May’s Options
It is Tuesday afternoon, February 14, 2012. Richard May, Assistant Treasurer at
American Digital Graphics (ADG), sits in his office on the thirty-fourth floor of the building that
dominates Rockefeller Plaza’s west perimeter. Its Valentine’s Day and Richard and his wife
have dinner reservations with another couple at Balthazar at 7:30. “I must get this hedging
memo done,” thinks May, “and get out of here. Foreign exchange options? I had better get the
story straight before someone in the Finance Committee starts asking questions. Let’s see,
there are two ways in which I can envisage us using options now. One is to hedge a dividend
due on September 15th from ADG Germany. The other is to hedge our upcoming payment to
Matsumerda for their spring RAM chip statement. With the yen at 78 and increasing I’m glad we
haven’t covered the payment so far, but now I’m getting nervous and I would like to protect my
posterior. An option to buy yen on June 10 might be just the thing.
Before we delve any further into Richard May’s musings, let us learn a bit about ADG,
and about foreign exchange options. American Digital Graphics is a $12 billion sales company
engaged in, among other things, the development, manufacture, and marketing of
microprocessor-based equipment. Although 30 percent of the firm’s sales are currently abroad,
the firm has full-fledged manufacturing facilities in only three foreign countries, Germany,
Canada, and Brazil. An assembly plant in Singapore exists primarily to solder Japanese
semiconductor chips onto circuit boards and to screw these into Brazilian-made boxes for
shipment to the United States, Canada, and Germany. The German subsidiary has developed
half of its sales to France, the Netherlands, and the United Kingdom, billing in euros. ADG
Germany has accumulated a cash reserve of €900,000, worth $1,178,100 at today’s exchange
rate. While the Hamburg office has automatic permission to repatriate €3 million, they have
been urged to seek authorization to convert another €1 million by September 15th. The firm has
an agreement to buy three hundred thousand RAM chips at ¥8000 each semi-annually, and it is
this payment that will fall due on June 10th.
The conventional means of hedging exchange risk are forward or future contracts.
These, however, are fixed and inviolable agreements. In many practical instances the hedger is
uncertain whether foreign currency cash inflow or outflow will materialize. In such cases, what
is needed is the right, but not the obligation, to buy or sell a designated quantity of a foreign
currency at a specified price (exchange rate). This is precisely what a foreign exchange option
provides.
A foreign exchange option gives the holder the right to buy or sell a designated quantity
of a foreign currency at a specified exchange rate up to or at a stipulated date.
The terminal date of the contract is called the expiration date (or maturity date). If the option
may be exercised before the expiration date, it is called an American option; if only at the
expiration date, a European option.
The party retaining the option is the option buyer; the party giving the option is the option
seller (or writer). The exchange rate at which the option can be exercised is called the exercise
price or strike price. The buyer of the option must pay the seller some amount, called the option
price or the premium, for the rights involved.
The important feature of a foreign exchange option is that the holder of the option has
the right, but not the obligation, to exercise it. He will only exercise it if the currency moves in a
favorable direction. Thus, once you have paid for an option you cannot lose, unlike a forward
contract, where you are obliged to exchange the currencies and therefore will lose if the
movement is unfavorable.
The disadvantage of an option contract, compared to a forward or futures contract is that
you have to pay a price for the option, and this price or premium tends to be quite high for
certain options. In general, the option’s price will be higher the greater the risk to the seller (and
the greater the value to the buyer because this is a zero-sum game). The risk of a call option
will be greater, and the premium higher, the higher the forward rate relative to the exercise price;
after all, one can always lock in a profit by buying at the exercise price and selling at the forward
rate. The chance that the option will be exercised profitably is also higher, the more volatile is
the currency, and the longer the option has to run before it expires.
Returning to Richard May in his Rockefeller Center office, we find that he has been
printing spot, forward and currency options and futures quotations from the company’s
Bloomberg terminal.
The option prices are quoted in U.S. cents per euro. Yen are quoted in hundredths of a
cent. Looking at these prices, Richard realizes that he can work out how much the euro or yen
would have to change to make the option worthwhile. Richard makes a mental note that ADG
can typically borrow in the Eurocurrency market at LIBOR + 1% and lend at LIBID.
“I’ll attach these numbers to my memo,” mutters May, but the truth is he has yet to come
to grips with the real question, which is when, if ever, are currency options a better means of
hedging exchange risk for an international firm than traditional forward exchange contracts or
future’s contracts. Please assist Mr. May in his analysis of currency hedging for his report to
ADG’s Finance Committee. In doing so, you may consult the highlighted market quotes in the
following attachments.
Solution:
ADG’s euro receivable
ADG has a €3,000,000 receivable in 214 days on September 15th. To assess alternative ways of
hedging, the following data are relevant: The current spot exchange rate (S)=$1.3088/€, 7-
month forward exchange rate (F)=$1.3090, the dollar interest rate (bid)=0.78% and euro interest
▪ Forward hedge
If ADG chooses to use forward contract, it just needs to sell its euro receivable at today’s
▪ Money market hedge
If ADG decides to use money market hedging, it first needs to borrow the present value (PV) of
its euro receivable at 2.40% interest rate (=1.40%+1.0%):
PV = (€3,000,000) / (1+0.024(214/360)) = 3,000,000 / 1.01427 = €2,957,802.
▪ Option hedge
If ADG chooses to hedge its euro receivable using currency options, it can purchase put options
on three million euros with a $1.31 strike price at the premium of 5.09 cents per euro. This
means that the firm has to spend the option cost upfront. The option costs, including the time
value of money, would be: 153,408 = (€3,000,000) ($0.0509) [1+0.0078 (214/360) ]. If the future
As can be seen from the following graph, forward hedging dominates money market hedging. If
Dollar receipt from euro receivable hedging alternatives
ADG’s yen payable
$ receipt
$
3,927,00
$
3,889,12
$
3,776,59
0
Forward
Money
market
Put option
$
1.31
S*=$
S7($/€)
ADG has a ¥2,400 million payable in 4 months. The relevant market data include: The current
spot exchange rate of $0.01274/¥, four-month forward exchange rate of $0.01274/¥, four-month
▪ Forward hedge
If ADG decides to use forward contract to hedge its yen payable, it just needs to purchase the
▪ Money market hedge
Money market hedging would require borrowing the PV of the yen payable in dollars,
$30,558,123.50 = [(¥2,400,000,000)/(1+0.0018(117/360)] ($0.01274), and converting the dollar
amount borrowed into yen and invest for four months at the yen interest rate to receive,
▪ Option hedge
In the case of hedging with option, ADG will need to buy call option on its yen payable. If ADG
decides to buy options with strike price set at $0.0127 per dollar trading for 3.11 cents per 100
As can be seen from the graph below, forward hedge dominates money market hedge as the
dollar cost will be always lower with forward hedge than with money market hedge. If the
exchange rate becomes lower than the indifference rate, S*=$0.0124, call option hedge would
Dollar cost from yen payable hedging alternatives
$ cost
$
31,227,78
$
30,719,012
$
30,576,000
0
Forward
Money
market
Call
option
0.012
4
S*=0.01
27
S4($/¥)
$ 747,783
