M3508 Exercises 1
October 2008
1. Spot USDJPY is trading at 105.00. The one year forward is trading at
102.00. Where will USDJPY be trading in one year’s time?
2. Recall that an FX rate XXXYYY = Bid/Offer gives the rate of YYY
per XXX. You can buy XXX/sell YYY at the offer price and sell
XXX/buy YYY at the bid price.
• EURUSD is trading at 1.3855/1.3860
• USDJPY is trading at 105.60/105.70
• EURJPY is trading at 145.50/145.65
You have 1 million EUR. Find the sure-thing arbitrage and calculate
how many EUR profit you can make, explaining the trades necessary
to achieve this.
3. (a) Does the existence of quadrilateral arbitrage between 4 currencies
necessarily imply the existence of triangular arbitrage? Justify.
(b) Using covered interest rate arbitrage, show that it is possible to
perform triangular arbitrage for FX forwards.
4. A carry trade is a foreign exchange trade where you borrow money in a
low-yielding currency (ie a low interest rate) and lend in a high-yielding
currency in an attempt to earn the difference called the carry. Write
a paragraph about the risks and arbitrage opportunities for this trade.
Illustrate this with an example.
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5. Free iPods
Anne lives in NY where the Apple store sells iPods for 200 USD, she
has 10,000 USD in cash. Ben in London can buy them for 100 GBP
and has 5,000 GBP in cash. The current exchange rate is 2 USD per
GBP. They could each buy 50 iPods today but instead they want to
use their financial knowledge to generate an arbitrage.
First they decide to exchange currencies today.
In one year’s time the exchange rate has moved to 1.5 USD per GBP.
Ben changes his 10,000 USD and has 6,667 GBP with which he buys
66 iPods.
Anne changes her 5,0000 GBP and has 7,500 USD with which she buys
37 iPods. Collectively they now have 103 iPods instead of the 100 if
they had not exchanged their currencies 1 year ago.
• How is this possible? What assumptions have we made?
• Calculate the number of iPods they can buy if the exchange rate
moves to n USD per GBP and show they always make a gain if
the exchange rate moves.
Note: this is an example of Siegel’s Paradox in action.
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