ADDITIONAL PROBLEMS 1

1.. You take a 1-year long position in an actual (US dollar-denominated) forward FX contract on yen at a forward FX rate of F1¥/$ = 100 ¥/$. The contract AMOUNT is $1 million. If the spot FX rate for the yen a year from now is X1¥/$ = 125 ¥/$, what is the US dollar gain (loss) on the long forward position on yen?

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2.. You established a short two-year forward FX contract on yen a year ago at a forward FX rate of 125 ¥/$. The contract’s AMOUNT is $1 million and the delivery time is a year from now. The current spot FX rate is 112 ¥/$. The one-year US dollar interest rate is currently 5% and the one-year yen interest rate is currently 1%. What is the MTM value in US dollars of your short forward position on yen?

That is, how much would you receive (or have to pay) in US dollars if you liquidated the forward FX position in the market today?

The following information is used in problems 3 through 5. You manage the corporate treasury for UTC. Assume that presently the spot FX rate is 1.80 $/£ and that the actual 1-year forward FX rate is 1.75 $/£. The 1-year US dollar interest rate is 4%; the 1-year pound sterling interest rate is 5%.

3.3. Explain how to create a synthetic long 1-year forward FX position on pounds.

4.4. What is the synthetic 1-year forward FX rate?

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5.. Which is better if you want to take a 1-year short forward FX position on pounds, an actual forward FX contract or a synthetic one?

The following information is used in problems 6 through 9. A US importer has a euro payable due in one year. The spot FX rate is 1.40 $/€ today. Today, the 1-year forward FX rate is 1.35 $/€. At time 0 (now), the importer can borrow or lend euros for the same one-year interest rate of 6%, and can borrow or lend US dollars for the same one-year interest rate of 4%. The spot FX rate a year from now turns out to be 1.30 $/€.

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6.. At time 0, the importer decides to hedge the FX transaction exposure of the euro payable with a forward FX contract with an AMOUNT equal to $100,000. If the importer’s forward FX position is settled by a difference check a year later at the delivery time, how much is the difference check for, and does the importer pay it or receive it?

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7.. In retrospect at time 1, is the importer glad he hedged with the forward FX position or does he regret the decision to hedge. Explain.

8.8. At time 0, the importer decides to hedge the FX transaction exposure of the euro payable with a money market hedge (―cash and carry strategy‖ to create a synthetic forward FX position.) What are the transactions of this hedge?

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9.9. Ignoring any possible transaction costs in our scenario, which alternative is better: a) hedge the payable’s FX exposure with the actual forward FX contract;

or b) hedge the payable’s FX exposure with the money market hedge? Explain.

1010.. Assume that presently the spot FX rate today is 1.44 $/£. The actual 1-year forward FX rate is presently 1.40 $/£. The 1-year US dollar interest rate is 5%;

the 1-year pound sterling interest rate is 7%. In the given assumptions, the covered interest rate parity (CIRP) condition is violated. A) Given the two interest rates and today’s actual spot FX rate, what should be the 1-year forward FX rate, if CIRP holds? B) Explain in detail the arbitrage you should perform to exploit the CIRP violation in the given information and to provide you with an arbitrage profit at time 0. What is the time-0 arbitrage profit for a forward FX position amount of

$1.40 million?

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1.. Z^¥ = ¥100 million; D¥$ = ¥100 million(0.008 $/¥ – 0.01 $/¥) = –$200,000. The long yen position thus loses $200,000.

2.2. The long forward position on yen would have an MTM value of (¥125 million/1.01)/(112 ¥/$) – $1 million/1.05 = $152,640. Since you are short, your MTM position is worth –$152,640.

3.3. Borrow US dollars (issue US dollar debt), buy spot pounds, and deposit the pounds.

4.4. (1.80 $/£)(1.04/1.05) = 1.783 $/£.

5.5. It is better in the case to sell pounds forward at the synthetic forward FX rate of 1.783 $/£ than at the actual rate of 1.75 $/£.

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6.. The forward FX contract SIZE = $100,000/(1.35 $/€) = €74,000 (rounded). The difference check to the long forward FX position is €74,000(1.30 $/€ – 1.35 $/€) = –$3700. The importer pays the check since he takes a long forward FX position on euros as a hedge of a euro payable.

7.7. Regret. The actual spot FX rate at time 1 turned out to be a lower FX price of the euro than the 1-year forward FX price of the euro at time 0.

8.8. Borrow US dollars for a year, spot exchange into euros at time 0, and deposit the euros for a year.

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9.9. The synthetic forward FX rate equals 1.40 $/€ (1.04/1.06) = 1.37 $/€. It would be cheaper to buy forward euros for 1.35 $/€ with the actual forward FX contract than via the synthetic route at 1.37 $/€.

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100.. A) (1.44 $/£)(1.05/1.07) = 1.413 $/£.

B) The actual forward FX value of the pound (1.40 $/£) is too low compared to the theoretical forward of CIRP (1.413 $/£). Thus buy pounds forward, i.e., take a long actual forward FX position on pounds, with contract size = £1 million. To cover, you forward short pounds synthetically: first borrow £1 mm/1.07 =

£0.935 million, to repay £1 million next year. Convert the pounds to US dollars today at the actual spot FX rate of 1.44 $/£ to get $1.346 million. You need only deposit today the PV of $1.4 million, which is $1.4 million/1.05 = $1.333, million in order to have the necessary $1.4 million amount to deliver against the forward FX obligation. Your time-0 arbitrage profit is thus $1.346 million minus

$1.333 million = $12,667.