International Financial Management
Spring, 2017
Homework Questions 1: Due date–Tuesday, Feb 21, 2017
Name:
Instructions:
• Read the questions carefully, write all your steps where necessary.
• You don’t have to computer-type the solution. However, the hand-written version has
to be reader-friendly.
• Hard copies of the solutions must be dropped in the TA’s box by 6PM on the due
date. No later submission will be accepted.
• You may work in groups of four or less, and only one solution set will be turned in
by each group. The grade on the problems turned by the group will be given to each
member of the group.
1. If the $/£ bid and ask prices are $1.50 and $1.51, respectively, the corresponding £/$
bid and ask prices are:
(a) £0.6667 and £0.6623
(b) $1.51 and $1.50
(c) £0.6623 and £0.6667
(d) cannot be determined with the information given
Answer: c) Rationale: £1/$1.51 ask price = £0.6623 bid price/$1; £1/$1.50 bid price
= £0.6667 ask price/$1.
2. The $/CAD spot bid-ask rates are $0.7560-$0.7625. The 3-month forward points are
12-16. Determine the $/CAD 3-month forward bid-ask rates.
(a) $0.7548-$0.7609
(b) $0.7572-$0.7641
(c) $0.7512-$0.7616
(d) cannot be determined with the information given
Answer: b)
Rationale: 12<16, so you want to add them to the spot bid-ask rates. Forward bid =
$0.7560 + 0.0012 = $0.7572; forward ask = $0.7625 + 0.0016 = $0.7641.
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International Financial Management
Spring, 2017
3. The SF/$ spot exchange rate is SF1.25/$ and the annual forward premium is 8 percent. What is the 180 day forward exchange rate?
(a) SF1.30/$
(b) SF1.20/$
(c) SF6.25/$
(d) None of the above
Answer: a)
Rationale:
F180 (SF/$) − S (SF/$) 360
F180 (SF/$) − 1.25
×
=
× 2 = 8%
S (SF/$)
180
1.25
F180 (SF/$) = 1.30
4. A formal statement of IRP is
(a)
1+i$
1+i£
=
F ($/£)
S($/£)
(b)
1+i$
1+i£
=
S($/£)
F ($/£)
(c)
1+i$
1+i£
=
F ($/£)−S($/£)
S($/£)
(d) F ($/£) − S($/£) = i$ − i£
Answer: a)
5. Suppose that the one-year interest rate is 5.0 percent in the Hong Kong, the spot
exchange rate is $1.20/e, and the one-year forward exchange rate is $1.16/e. What
must one-year interest rate be in the euro zone?
(a) 5.0%
(b) 1.09%
(c) 8.62%
(d) None of the above.
Answer: c)
F ($/e)
1 + i$
1 + 5%
1.16
=
=
=
⇒ ie = 8.62%
S($/e)
1 + ie
1 + ie
1.20
6. Assume you are a trader with Deutsche Bank. From the quote screen on your computer terminal, you notice that Dresdner Bank is quoting e0.7627/$1.00 and Credit
Suisse is offering SF1.1806/$1.00. You learn that UBS is making a direct market
between the Swiss franc and the euro, with a current e/SF quote of e0.6395/SF1.00.
Show how you can make a triangular arbitrage profit by trading at these prices (ignore
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International Financial Management
Spring, 2017
bid-ask spreads for this problem.) Assume you have $5,000,000 with which to conduct
the arbitrage. What happens if you initially sell dollars for Swiss francs? What e/SF
price will eliminate triangular arbitrage?
Solution:
The implied cross rate here is
S (e/SF ) =
S (e/$)
0.7627
=
= 0.6460 > 0.6395
S (SF/$)
1.1806
To make a triangular arbitrage profit, we want to buy SF at e0.6395 then sell
at e0.6460. The Deutsche Bank trader would sell $5,000,000 to Dresdner Bank
at e0.7627/$1.00. This trade would yield e3,813,500= $5,000,000 × 0.7627. The
Deutsche Bank trader would then sell the euros to buy Swiss francs to Union Bank of
Switzerland at a price of e0.6395/SF1.00, yielding SF5,963,253 = e3,813,500/0.6395.
The Deutsche Bank trader will resell the Swiss francs to Credit Suisse for $5,051,035.53
= SF5,963,253/1.1806, yielding a triangular arbitrage profit of $51,035.53.
If the Deutsche Bank trader initially sold $5,000,000 for Swiss francs, instead of euros,
the trade would yield SF5,903,000 = $5,000,000 × 1.1806. The Swiss francs would in
turn be traded for euros to UBS for e3,774,969= SF5,903,000 × 0.6395. The euros
would be resold to Dresdner Bank for $4,949,480.14 = e3,774,969/0.7627, or a loss
of $50,519.86. Thus, it is necessary to conduct the triangular arbitrage in the correct
order.
Note: the S(e/SF) cross exchange rate should be 0.6460. This is an equilibrium rate
at which a triangular arbitrage profit will not exist.
7. The current spot exchange rate is $1.95/£ and the three-month forward rate is
$1.90/£. Based on your analysis of the exchange rate, you are pretty confident that
the spot exchange rate will be $1.92/£ in three months. Assume that you would like
to buy or sell £1,000,000.
(a) What actions do you need to take to speculate in the forward market? What is
the expected dollar profit from speculations?
(b) What would be your speculative profits in dollar terms if the spot exchange rate
actually turns out to be $1.86/£?
Solution: If you believe the spot exchange rate will be $1.92/£ in three months, you
should buy £1,000,000 forward for $1.90/£. Your expected profit will be: $20,000 =
£1,000,000× ($1.92 -$1.90).
If the spot exchange rate actually turns out to be $1.86/£, your profit will be: -$40,000
= £1,000,000× ($1.86 -$1.90).
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International Financial Management
Spring, 2017
8. Suppose that the treasurer of IBM has an extra cash reserve of $100,000,000 to invest
for six months. The interest rate is 8 percent per annum in the United States and 7
percent per annum in Germany. Currently, the spot exchange rate is e1.01 per dollar
and the six-month forward exchange rate is e0.99 per dollar. The treasurer of IBM
does not wish to bear any exchange risk. Where should he/she invest to maximize
the return?
Solution: The market conditions for six-month horizon are: i$ = 4%; ie = 3.5%; S =
e1.01/$; F = e0.99/$.
If $100,000,000 is invested in the U.S., the maturity value in six months will be
$104,000,000 = $100,000,000 (1 + .04).
Alternatively, $100,000,000 can be converted into euros and invested at the German
interest rate, with the euro maturity value sold forward. In this case the dollar maturity value will be $105,590,909 = ($100,000,000 × 1.01)(1 + .035)(1/0.99). Clearly,
it is better to invest $100,000,000 in Germany.
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