Test # 1
(FX market, International parity conditions, FX derivatives)
This is an open-book assignment that is due by 11:59pm ET on Sunday January 24, 2021. Please
submit your work on Canvas or send it as an attachment via email to [email protected]. The test
contains two parts. Answer all questions. Show all your work in order to receive partial credit.
Part I: This part contains 6 questions. Total points = 30 pts (i.e., 5 pts per question).
(1) Suppose that you intend to hedge a CHF cash flow that is expected to materialize sometime
within the next three months. You are contemplating whether you should:
a. use a forward hedge by contacting a bank and setting up a forward contract on CHF
that expires in 3 months, or
b. use a futures hedge by trading CHF futures on the futures exchange in Chicago.
What are the factors that will lead you to prefer one versus the other alternative?
(2) Suppose that the current spot exchange rate is S=1.26$/€. You observe the following
American style options:
a. an American put on the Euro with K=1.30$/€, 3 months till expiration that is selling
in the market for P=0.04$/€.
and
b. an American call on the Euro with K=1.20$/€, 3 months till expiration is selling in
the market for C=0.05$/€.
How would you respond to this situation?
(3) Suppose that you expect the US$ value relative to the Euro to remain fairly stable over the
next few months. In your opinion, there is a very low and equal probability of either a
positive ($ appreciation) or negative ($ depreciation) change in the value of the Euro. How
can you devise a trading strategy that is tailored along your convictions? Show in a graph (or
with a detailed explanation) how that strategy will work and explain the potential pitfalls, if
any.
(4) Suppose you decided to speculate in the FX market. You are particularly bullish about some
of the Emerging markets currencies, such as the Brazilian Real, Indian Rupee, and Korean
Won. Describe what are the alternative investment instruments and strategies you would
consider.
(5) The WSJ Dollar index has been on a gradual decline over the past year or so. What are the
determinants of the value of the dollar in the short run and in the long run?
(6) Large US trade deficits have persisted for a long period of time. Provide a brief background
on this issue and your assessment on whether this constitutes a real problem for the U.S.
economy and the long term value of the US dollar.
Part II: Problem solving. Answer all 10 problems. Total points = 70 pts (i.e., 7 pts for each problem)
(1) PSG Inc., a U.K. manufacturer, is expecting an inflow of 18.3 million US-$ within the next four
months. Today’s spot exchange rate is 0.7407 British pounds (£) per US-$. PSG decides to hedge
using options. The £ interest rate is 1.79%. PSG contacts Citicorp which offers the following options
on the US-$:
- American call option on the US-$ with T=3 months, K=0.74 £/$, and price C=0.025 £/$
- American put option on the US-$ with T=3 months, K=0.74 £/$, and price P=0.012 £/$
- American call option on the US-$ with T=6 months, K=0.74 £/$, and price C=0.029 £/$
- American put option on the US-$ with T=6 months, K=0.74 £/$, and price P=0.015 £/$
Answer the following questions, assuming that these options have no resale value, and ignoring
transactions costs.
a) Which option should PSG choose?
b) Suppose that 5.5 months later PSG receives the 18.3 million US-$ payment. At that time (t=5.5
months) the spot exchange rate is 0.68 £/$. What should PSG do? How many £ per US-$ will they
receive net of the expense for the purchase of the option?
c) Now, suppose that 5.5 months later (i.e., at the time when PSG will receive 18.3 million US-$) the
spot exchange rate is 0.78 £/$. What should PSG do? How many £ per US-$ will they receive net of
the expense for the purchase of the option?
(2) Suppose that you observe the following:
The price of a call option on the Euro (€) is 0.055 $/€. The price of a put option on the € is 0.045 $/€.
Both options have 92 days left to expiration and a strike price of 0.85 $/€. The current spot rate is
0.89 $/€. The $-risk free rate is 3.5% and the €-risk free rate is 3.75%.
a) Is there an arbitrage opportunity? Why?
b) Calculate the arbitrage profits and show the arbitrage transactions and corresponding cash flows
at t=0 (now) and at t=T=92 days later.
(3) ABC Inc., a US importer of European products wishes to devise a hedge of a 32 million Thai Bhat
(Bt) outflow, expected in 3 months. ABC’s financial experts suggest that this exposure can be hedged
using different combinations of € (Euro), CHF (Swiss Franc), ¥ (Yen) and £ (British pound) futures
contracts. They presented the following results of their analysis to the CFO:
ΔS$/Bt = 0.03 + 0.95 Δf
$/CHF + 2.55 Δf
$/¥
[t=1.34] [t=7.50] [t=2.73] R2=0.87
ΔS$/Bt = 0.03 + 0.47 Δf
$/€ – 1.55 Δf
$/£
[t=1.31] [t=12.50] [t=1.41] R2=0.93
Upon seeing the above, the CFO got confused and did not know what to do. All he remembered is
that the size of the €, CHF, ¥, and £ futures contracts is 100,000 €, 125,000 CHF, 12,500,000 ¥ and
62,500 £, respectively. Can you help him devise the hedge? How many contracts does ABC need to
buy/sell if its primary goal is to reduce the exposure as much as possible?
(4) Suppose you are a Swiss importer of olive oil from Greece. You are preparing to import an olive
oil shipment of 100,000 lbs that will require payment in Euro (€) in 3 months. The payment’s exact
amount will depend on both the CHF/€ exchange rate, as well as the price for oil, which is a function
of uncertain supply conditions in Greece. You project the following six scenarios with regards to the
price of olive oil in 3 months:
Scenario Price (€/lb of oil)
1 2.1
2 2.3
3 3.8
4 1.8
5 3.0
6 2.8
a) What can you do today if your goal is to completely hedge this €-exposure?
b) Suppose that 3 months from now, scenario # 6 materializes. What will you do?
(5) Mainz GmbH, a German importing firm anticipates receiving ¥189.3 million in 6 months.
Mainz’s management team is worried about the course of the ¥/€ exchange rate over the next 6
months and decides to hedge. The current spot and forward rates are S0=125 ¥/€ and Ft=6 months = 121
¥/€. The €-interest rate is 0.36% and the ¥-interest rate is 0.28%.
a) Compute the € cash flow to Mainz GmbH if it hedges its position using the forward market.
b) Compute the € cash flow to Mainz GmbH if it hedges its position using the money market.
c) Which of the two above hedges is best for Mainz GmbH.?
Alternatively, Mainz GmbH is contemplating the use of an options hedge. Sanwa bank is offering to
Mainz GmbH the following options:
i) Call option on ¥189.3 million at K=125 ¥/€, with a 3.8% premium (price as a percent
of current spot rate).
ii) Put option on ¥189.3 million at K=125 ¥/€, with a 3.15% premium (price as a percent
of current spot rate).
d) Which one is the right option to choose? What is the upfront cost of the option hedge?
e) Compute the break-even rate between the options hedge and the better one of the forward
and money market hedges. How does the break-even rate help you decide on which hedge to use?
(6) Suppose you are given the following exchange rates:
0.0094/0.0098 $/¥
60.7492/60.7512 ¥/CHF
0.5837/0.5841 $/CHF
Is there a triangular arbitrage opportunity? Describe the steps involved if you can start with 1
million CHF.
(7) Suppose the current exchange rates between the US dollar ($) and the Indian rupee (INR), Thai
Bhat (THB) and Philippine peso (PHP) are 68.0724 INR/$, 32.1836 THB/$, and 52.3803 PHP/$,
respectively. In addition, you observe that a Big Mac costs 180.00 INR in India, 119.00 THB in
Thailand, and 134.00 PHP in the Philippines. If the US average price of a Big Mac is 5.28$,
a) What would the Big Mac Index imply for the over- or undervaluation of these currencies vis-à-vis
the US$?
b) If you were a foreign exchange trader, what would you do in response to the answer to part a) ?
(8) Suppose that the spot and the forward exchange rates between the UK pound (£) and the Euro (€)
are S0=0.5108 £/€ and Ft=3 months=0.5168 £/€. The time to maturity of the forward contract is 3
months. The annual interest rate of £-denominated Eurocurrency market deposits is 4.08%. The
annual interest rate of €-denominated, 3-month Eurocurrency market deposits is 3.15%.
a) Examine whether there exists an arbitrage opportunity.
b) Devise an arbitrage strategy. Describe the transactions and calculate the arbitrage profits.
(9) BXP Inc., a UK importing firm anticipates an outflow of 186 million Danish Krone (DKK) in 6
months. BXP’s managers are worried about the course of the DKK/£ exchange rate over the next 6
months and they decide to hedge. The current spot and forward rates are S0=6.1718 DKK/£ and Ft=6
months=6.2035 DKK/£. BXP can borrow/lend at a £-interest rate of 3.57% and a DKK-interest rate of
5.15%.
a) How can BXP hedge its position using the forward market? Calculate the 6-month ahead cash flow
BXP can lock in with the forward hedge.
b) How can BXP hedge its position using the money markets? Calculate the 6-month ahead cash flow
BXP can lock in with the money market hedge.
c) Why do the two hedges result in different amounts that can be “locked in”? Which of the two
hedges is best for BXP Inc.? Would things be different if BXP was attempting to hedge an inflow of
DKK?
(10) You are a German businessman who is expecting to receive a payment of 4.83 million South
African Rand (SAR) nine months from today. The spot exchange rate is 6.11 SAR/€, the expected
annual inflation rate in South Africa is 10.5% and in the European Union it is 2.16%.
a) Based on the above, what is your best estimate of the spot exchange rate that will prevail nine months from now?
b) How would you hedge your position if you were to use the money market (Note: describe only)?
c) Suppose that nine months later the spot rate is 6.15 SAR/€ and that the inflation rates forecasts turned out to be accurate. Calculate the real exchange rate and the real % change in the value of the SAR over the past nine months.