# Project 1 - Hedging - Solutions

```Concordia University
FINA 470 – International Finance
SOLUTIONS FOR:
PROJECT 1 – EXCHANGE RATE RISK HEDGING
PROF. THOMAS WALKER, PH.D.
DEPARTMENT OF FINANCE
CONCORDIA UNIVERSITY
Solutions for Project 1
February 10, 2020
Concordia University
FINA 470 – International Finance
SOLUTIONS FOR PROJECT 1 – EXCHANGE RATE RISK HEDGING
Question a.)
The Swiss beer exporter faces the risk that the US Dollar might depreciate against the
Swiss Franc between September 18th and October 28th. If the dollar depreciated, then on the
day of payment the Swiss beer exporter would actually get less Swiss Francs for the exported
beer than he would have gotten (and has been expecting) on the day the contract was entered
into. In addition, the beer exporter faces the risk that the U.S. importer might default on its
payment obligation, i.e. that the payment for its exported beer won’t come through.
Question b.)
Because the beer exporter has to fear that the dollar depreciates, he should take a long
position and buy Swiss Franc futures to offset any possible losses (but also gains) in the spot
market. Swiss Franc futures are only sold for SFR 125,000 each. At the date the contract is
done, the beer exporter can expect to receive approximately
70,000 barrels * US\$ 18.75 / barrel * SFR 1.5090/US\$ = SFR 1,980,562.50.
Given the futures contract size of 125,000 SFR/contract, the number of futures
contracts needed to hedge the above amount is
SFR 1,980,562.50 / SFR 125,000/futures contract = 15.84 futures contracts
Thus, the Swiss beer exporter can either decide to buy 15 futures contracts with a
value of 15 * SFR 125,000 = SFR 1,875,000 or sixteen futures contracts with a value of 16 *
SFR 125,000 = SFR 2,000,000. In other words, the beer exporter can either choose to
“underhedge” by buying only 15 futures contracts or to “overhedge” by buying 16 futures
contracts. As noted in class, it makes sense to choose the closest integer number to maximize
the accuracy of the hedge. In the following calculations we thus assume that the company
buys (goes long) 16 futures contracts.
____________________________________________________________________________________________
Prof. Thomas Walker, Ph.D.
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Concordia University
FINA 470 – International Finance
Since futures are only traded for certain months, the beer exporter has to buy
December futures, because December is the closest possible month for the beer exporter to
sell his 70,000 barrels * US\$ 18.75 / barrel = US\$ 1,312,500 in the spot market on October
28th and close out his futures position.
On the date of liquidation, when the beer exporter receives the payment from his
counterpart, he should exchange the US\$ he receives and make some profit on them since the
US\$ actually appreciated against the SFR. Also, he should close his position by selling the
future contracts on October 28th. The beer exporter should not keep the US\$ until the delivery
date in December, because this would involve further speculation, which is not in the riskminimizing sense of hedging. Also, if the company didn’t exchange its dollar payment into
Swiss Francs on the liquidation date, it might be short of Swiss Francs to pay its employees or
take on other projects.
Question c.)
If the beer exporter decided to hedge with currency options, he has to buy SFR call
options in the US. The Wall Street Journal provides us with the necessary data for this case.
Say the exporter buys SFR call options on the Philadelphia Stock Exchange, then he has to
decide how many options he wants to buy.
Similar to question b) above, we can calculate the number of call option contracts
needed as follows:
SFR 1,980,562.50 / SFR 62,500/option contract = 31.69 option contracts
Thus, if he wants to hedge with options, he can either decide to buy 31 call options
with a value of 31 * SFR 62,500 = SFR 1,937,500 or 32 futures contracts with a value of 32 *
SFR 62,500 = SFR 2,000,000. In other words, the beer exporter can again either choose to
“underhedge” by buying only 31 call options or to “overhedge” by buying 32 call options. As
before, we round to the closest integer and thus buy 32 call options.
On the date of liquidation, the beer exporter must buy Swiss Francs in the spot market
and sell his call options for the current market premium of 1.33 cents per SFR. Since the SFR
____________________________________________________________________________________________
Prof. Thomas Walker, Ph.D.
Page 2
Concordia University
FINA 470 – International Finance
has appreciated until October 28th and the options are worth less than what we paid for them
initially, the beer exporter will incur a loss when selling them.
Question d.)
Our unhedged gain/loss can be calculated in the following way:
(70,000 barrels * US\$ 18.75/barrel) * (SFR 1.5193/US\$ - SFR 1.5090/US\$) =
US\$ 1,312,500 * SFR 0.0103/US\$ = SFR 13,518.75 (Gain)
Question e.)
Suppose the beer exporter would have bought 16 SFR futures with a total contract
value of SFR 2,000,000, then we can calculate his profit/loss in the futures market as follows:
Value of futures position on Sept. 18 (V0):
(SFR 2,000,000 * US\$ 0.6666/SFR) * SFR 1.509/US\$ = SFR 2,011,798.80
Value of futures position on Oct. 28 (V1):
(SFR 2,000,000 * US\$ 0.6601/SFR) * SFR 1.5193/US\$ = SFR 2,005,779.86
Profit/loss on futures:
V1 – V0 = SFR 2,005,779.86 - SFR 2,011,798.80 = - SFR 6,018.94 (Loss)
Thus, the net gain/loss would have been:
SFR 13,518.75 - SFR 6,018.94 = SFR 7,499.81 (Gain)
____________________________________________________________________________________________
Prof. Thomas Walker, Ph.D.
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Concordia University
FINA 470 – International Finance
Question f.)
X=65 Dec. options on Sept. 18th:
X=65 Dec. options on Oct. 28th:
With the premiums above and given that the beer exporter buys 32 options, we can
calculate the gain/loss on the options position as follows:
Value of options position on Sept. 18 (V0):
(SFR 2,000,000 * US\$ 0.0183/SFR) * SFR 1.509/US\$ = SFR 55,209.40
Value of options position on Oct. 28 (V1):
(SFR 2,000,000 * US\$ 0.0133/SFR) * SFR 1.5193/US\$ = SFR 40,413.38
Profit/loss on options:
V1 – V0 = SFR 40,413.38 - SFR 55,209.40 = - SFR 14,816.02 (Loss)
Thus, the net gain/loss would have been:
SFR 13,518.75 - SFR 14,816.02 = - SFR 1,297.27 (Loss)
Question g.)
Our results indicate that we achieved a net loss by hedging with options while we made
some money by hedging with futures. In addition, we could better offset changes in the firm’s
profitability which were due to a rising Dollar versus the Swiss Franc. Nevertheless, we should
be careful not to generalize these results, i.e. we can not say that this is always the better
alternative. In a declining exchange rate scenario, hedging with futures generally provides the
closest offset and thus the best protection. Options, however, provide a lesser degree of
protection in such a scenario, but will better preserve profits in a rising exchange rate scenario.
____________________________________________________________________________________________
Prof. Thomas Walker, Ph.D.
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Concordia University
FINA 470 – International Finance
Generally, the closer the net loss or gain to zero, the better the goal of hedging has been
fulfilled.
On a related note, because options are denominated in half the amounts of future
contracts (SFR 62,500 versus SFR 125,000), they can often better meet the exact amount that
a company wants to hedge. Thus, the amount of currency that is “overhedged” or
“underhedged” is usually lower. In addition to that, there are usually more option contracts
available (like over-the-counter contracts) that might better fit a company’s specific needs.
We always have to consider that hedging is not meant for speculative purposes, rather
it is a way for internationally operating companies to reduce their currency risk, which can
either incur a loss or a profit for them. Although in some cases a company might be better off
by using one approach or another, we should always consider which hedging strategy was
most successful in reducing the impact that fluctuating and volatile currencies might have on
their revenues.
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Prof. Thomas Walker, Ph.D.
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