Problem Set # 1
PART 1: FX-markets, International Parity conditions
1) You are interested in buying Swedish krona (SK). Your bank quotes “SK7.5050/$ Bid
and SK7.5150/$ Ask”. What would you pay in dollars if you bought SK 10,000,000 at
the current spot rate?
2) The following outright quotations are given for the Canadian dollar:
Bid (C$/$) Ask (C$/$)
Spot rate 1.2340 1.2350
One moth forward 1.2345 1.2365
Three moths forward 1.2367 1.2382
Six months forward 1.2382 1.2397
Assume you reside in the United States. Calculate forward quotes for the Canadian dollar
as an annual percentage premium or discount. Would a foreign exchange trader in
Canada get a different answer if asked to calculate the annual percentage premium or
discount on the U.S. dollar for each forward rate? Why?
3) Calculate appreciation or depreciation in each of the following:
a) If the dollar depreciates 10% against the yen, by what percentage rate does the
yen appreciate against the dollar?
b) If the dollar appreciates 1,000% against the ruble, by what percentage point
does the ruble depreciate against the dollar?
4) Suppose that at time t=0 the dollar per yen spot rate S0
$/¥ is 0.0100 $/¥ and that the yen
appreciates 25.86 percent during the next period.
a) What is the closing spot rate in dollars per yen, S1
$/¥?
b) By what percentage does the dollar depreciate against the yen?
5) Dow Chemical is to deliver chemicals to an Indian firm in one year and is supposed to
receive 40 million rupee (INR) at the time of delivery. The current exchange rate is 34.5
rupee per dollar (INR/$) and the one year-forward rate is 40 rupee per dollar (INR/$).
Dow’s one-year interest rates are 18% for rupee funds and 4% for dollar funds.
Suppose that Dow decides to hedge its exposure to the rupee. What are the alternatives
available to Dow based on the information given? Which hedge is optimal for Dow?
6) The peso is quoted in direct terms at 28.7356 ¥/Ps BID and 28.7715 ¥/Ps ASK in
Tokyo. The yen is quoted in direct terms at 0.03416 Ps/¥ BID and 0.03420 Ps/¥ ASK in
Mexico City.
a) Calculate the bid/ask spread as a percentage of the bid price from a Japanese
and from a Mexican perspective.
b) Is there an opportunity for profitable arbitrage? If so, describe the necessary
transactions using a ¥ 1 million starting amount.
7) The real rate of interest on bank loans and deposits is 2% in both the UK and the US.
Inflation in the US is 6%. In equilibrium, what is the UK inflation rate?
8) As a percentage of an arbitrary starting amount, about how large would transactions
costs have to be to make arbitrage between the exchange rates S0
SFr/$ = 1.7223 SFr/$,
S0
$/¥ = 0.009711 $/¥, and S0
¥/SFr = 61.740 ¥/SFr unprofitable?
9) You are free to invest in any currency. You can trade at the following prices:
Spot rate, Russian ruble per dollar 20 RUB/$
6 month forward rate for rubles 22 RUB/$
6-month Russian interest rate 18%
6-month U.S. interest rate 6%
a) Is covered interest arbitrage worthwhile? If so, explain the steps and compute the
profit.
b) Suppose that there is no forward market for the Russian ruble. Explain how an
investor can engage in “uncovered” interest arbitrage and whether this is a true
arbitrage or not.
10) Suppose that S0
$/₤ = 1.25$/₤, F1
$/₤ = 1.20$/₤, i₤ = 11.56% and i$ = 9.82%. You are to
receive 100,000₤ on a shipment of goods in one year. As a US-based firm you want to
avoid foreign exchange risk.
a) Form a forward market hedge. Identify which currency you are buying and
which currency you are selling forward. When will currency actually change
hands? Today? Or, in one year?
b) Form a money market hedge that replicates the payoff on the forward contract
by using the spot currency and the Euro-currency markets. Identify each contract
in the hedge. Does this hedge eliminate the foreign exchange risk?
c) Are the currency and Euro-currency markets in equilibrium? How would you
arbitrage the difference from the parity condition?
PART 2: FX options and FX futures
1) You want to hedge the Brazilian real (BRR) value of a 1 million Canadian dollar
(CAD) inflow using futures contracts. On Brazil’s exchange, there is a futures
contract for US$100,000 at 1.5 BRR/US$.
a) Your assistant runs a bunch of regressions:
- ΔS [BRR/CAD] = α1 + β1 Δf [US$/BRR]
- ΔS [BRR/CAD] = α2 + β2 Δf [BRR/US$]
- ΔS [CAD/BRR] = α3 + β3 Δf [BRR/US$]
- ΔS [CAD/BRR] = α4 + β4 Δf [US$/BRR]
Which regression is relevant to you?
b) If the relevant β is 0.83 how many contracts do you buy/sell?
c) We assumed that there was a $ futures contract in Brazil, with a fixed number
of US$ (100,000 units) and a variable BRR/US$ price. What f there is no
Brazilian futures exchange? Then, you’d have to go to a US exchange, where
the number of BRR per contract is fixed (at, say, 125,000) rather than the
number of US$. How many US$/BRR contacts will you buy?
2) A charitable organization has issued a bond that gives the holder the option to cash in
the principal as either £10,000 or €20,000. This asset can be viewed as a £10,000
bond plus a call on €20,000 with a strike price K=0.5£/€
a) Can the bond also be viewed as a € bond plus an option?
b) Explain how the two equivalent views are just an application of the Put-Call
parity
c) Suppose that you observe the following:
The price of a call option on the European Euro (€) is 0.055 $/€. The price of a put
option on the € is 0.045 $/€. Both options have 135 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%.
i) Is there an arbitrage opportunity? Why?
ii) Calculate the arbitrage profits and show the arbitrage transactions and
corresponding cash flows at t=0 (now) and at t=T=135 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 (EU),
SF , ¥ and £ futures contracts. They presented the following results of their analysis
to the CFO:
i) ΔS
$/Bt = 0.03 + 0.95Δf
$/SF
- 2.55Δf
$/¥
[t=1.34] [t=7.50] [t=2.73]
R
2=0.87
ii) ΔS
$/Bt = 0.03 + 0.47Δf
$/EU - 1.55Δf
$/£
[t=1.31] [t=2.50] [t=1.41]
R
2=0.33
Upon seeing the above, the CFO got confused and did not know what to do. All he
remembered is that the size of the EU, SF , ¥ and £ futures contracts is 100,000 EU,
125,000 SF, 12,500,000 ¥ and 62,500 £, respectively. Can you help him devise the
hedge? How many contracts does ABC need to buy/sell?
4) D-U Inc., an Australian manufacturer, is expecting an outflow of 83 million US-$
within the next four months. Today’s spot exchange rate is 1.25 Australian dollars
(A$) per US-$. D-U Inc. decides to hedge using options. The A$ interest rate is
5.79%. They contact Citi which offers the following options on the US-$:
a) American call on the US-$ with T=3 months, K=1.25 A$/US$, price
C=0.12A$/US$
b) American put on the US-$ with T=3 months, K=1.25 A$/US$, price P=0.10
A$/US$
c) American call on the US-$ with T=6 months, K=1.25 A$/US$, price C=0.14
A$/US$
d) American put on the US-$ with T=6 months, K=1.25 A$/US$, price P=0.115
A$/US$
Answer the following questions, assuming that these options have no resale value, and
ignoring transactions costs.
i) Which option should D-U Inc. choose?
ii) Suppose that 3.5 months later (i.e., at the time when D-U Inc. will have to pay
83 million US-$) the spot exchange rate is 1.36 A$/US-$. What should D-U
Inc. do? How much will D-U inc. have to pay, in terms of A$ per US-$?
iii) Now, suppose that at the time D-U Inc. will have to pay the 83 million US-$
(i.e. 3.5 months later) the spot exchange rate is 1.19 A$/US-$. What should DU Inc. do? How much will D-U Inc. pay in terms of A$ per US-$?
5) On October 20, you sold 10 futures contracts for 100,000 Canadian dollars (CAD)
each at a rate of 0.75 US$/CAD. The subsequent settlement prices are shown below.
October 21 22 23 24 27 28 29 30
Futures rate 0.74 0.73 0.74 0.76 0.77 0.78 0.79 0.81
a) What are the daily cash flows from marking to market?
b) What is the total cash flow from marking to market (ignoring discounting)?
c) If you deposit US$75,000 into your margin account, and your broker requires
US$50,000 as maintenance margin, when will you receive a margin call and how
much will you have to deposit?
6) You hold a foreign exchange asset that you have hedged with a put. Show graphically
how the put limits the potential losses created by low exchange rates, without
eliminating the potential gains from high rates.
7) You have covered a foreign exchange debt using a call. Show graphically how the
call limits the potential losses created by high exchange rates, without eliminating the
potential gains from low rates.
Sample Solution