Chapter 1: Globalization and The Multinational Firm
1. List 3 unique aspects of international business (no need to explain)
- Expanded opportunity set and comparative advantage
- Additional Risks (Exchange risk, Political risk)
- Market imperfections
2. Differentiate between absolute advantage and comparative advantage.
=> Absolute advantage is based on the production efficiency for each industry between the
two countries, while comparative advantage is comparing the production efficiency across
industries between the two countries.
3. Country A has an opportunity cost of 2 yards of textiles per one pound of food, and Country B has an
opportunity cost of 3 yards of textiles per one pound of food. Determine the comparative advantage, and
explain how free trade could enhance the well-beings of these countries. (You may want to make up
numbers to construct the input-output table).
=> Assuming that each country has the same amount of resources (100) and each country
splits its resources evenly between the two products, A may have 50 pounds of food and 100
yards of textiles (note that we satisfy 2 yards of textiles per one pound of food), and B may
have 50 pounds of food and 150 yards of textile. Since B has a comparative advantage in the
production of textiles, B can get specialized in the textile production and A can get
specialized in the food production. In this case, the world production of textiles can be
increased from 250 yards to 300 yards, while the world production of food remains the same
at 100 pounds.
4. a) How many SFs can you get for 20 dollars if SF/$=1.5?
b) If $ value doubles, then how much SF is up against $?
c) yen/$ was 201.6 in 1948 and it is now 108.2. How much yen has appreciated from 1948?
d) yen/$ = 108.2, BP/$ = 0.548. What is the BP/yen?
=> a) $20*1.5 (SF/$) = 30 SFs
b) $1/SF -> $0.5/SF => (0.5 – 1)/1 = -0.,5 It is up -50%
𝑆1−𝑆𝑜
.00924−.00496
.00428
c) So=1/201.6, S1=1/108.2,
=
= .00496 = .8629 =
𝑆𝑜
.00496
86.29% 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑒𝑙𝑦, 86.32% exactly
d) yen/$ = 108.2, BP/$ = 0.5480 .5480 BP/$ * 1/108.2 $/Yen = .005065
5. Differentiate between:
a) Linear vs. log scales
b) Standard deviation vs. coefficient of variation
=> a) Linear scales evaluate an absolute value change, whereas logarithm scales evaluate the
percent change.
b) Both are measure of dispersion of a set of data from its mean, but coefficient of variation
is considered as a better tool to evaluate volatility as it is independent of the level (Absolute
measure of volatility, relative measure of volatility & level free. Example: standard deviation
tends to large for a variable with a greater magnitude, while coefficient of variation is looking at
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a % change. A fat person tends to have a greater change in the weight (gaining or losing 5
pounds is an everyday event) than a skinny person. To be fair, we need to make it a level free.
That is what percentage of weight (instead of how many pounds) each person gain or lose a
day).
6. (a) How many SFs can you get for 20 dollars if $/SF=0.8?
(b) If the value of SF increases 30%, then how much $ is up against SF?
(c) Yen/$ was 133.59 in Feb 2002, depreciated about 18.06% from two years ago. What was
the yen/$ rate in Feb 2000?
(d) If yen/$ = 108.2, yen/BP = 197.45, what is the $/BP rate?
=> (a) 20*(1/.8)= 25
(b)Let’s assume that So=$1/SF, then a 30% appreciation of SF (against $)=> S1
=
$1.3/SF. $ appreciation rate against SF=(So – S1)/S1 = (1-1.3)/1.3= -23%
(c) Since the European term is given, S1 = 1/133.59 = 0.0074856. Yen appreciation
rate against $ = (S1 – So)/So = (0.0074856 – So)/So = -0.1806 => So =0.0074856/0.8194
= $0.00914/yen. Yen/$ rate in Feb. 2000 = 1/0.00914 = 109.41
(d) $/BP = ($/yen)*(yen/BP) =(1/108.2)*197.45 = 1.82486
7. 1) How many dollars does it take to get 10 SFs if SF/$=1.4?
2) If the price of a Twinkie goes up 25%, how much the dollar has lost its value?
=> 1) $7.143
2) Let’s say, the price of Twinkie increases from $1/TW to $1.25/TW. $ appreciate rate
against TW = (1-.1.25)/1.25 = > 20% drop.
8. Using the information given in the table below, provide your answers.
1) What is the yen/US$ exchange rate?
2) What would be the AU$/Can $ exchange rate?
Currency U.S. $
Last Trade N/A
¥en
11:29am
ET
1 U.S. $ = 1
116.3750 0.7844
1 ¥en
= 0.008593 1
1 Euro = 1.2749
Euro
11:29am
ET
Can $
11:29am
ET
U.K. £
11:29am
ET
AU $
11:29am
ET
1.1170
0.5262
1.3303
Swiss
Franc
11:29am
ET
1.2382
0.006740 0.009598 0.004521 0.011431 0.010640
148.3607 1
1.4239
0.6708
1.6960
1.5785
=> 1) 116.375
2) AU$/Can$, use a cross rate = (AU$/US$)*(US$/C$) = 1.3303 * (1/1.1170)=1.191
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9. Given the information in the following table.
What is the euro/C$ cross rate of 9/13?If the C$ has appreciated against US$ 2% from 8/14 to
9/14, what is the US$/C$ rate a month ago?
PACIFIC Exchange Rate Service
YYYY/MM/DD
Wdy
CAD/USD
EUR/USD
2453276
2008/09/13
Mon
1.2737
0.81252
2453277
2008/09/14
Tue
1.2755
0.81273
=> euro/C$ = (euro/US$) * (US$/C$) = 0.81252*(1/1.2737) = .6379
US$/C$ of 9/14 = S1 = 1/1.2755 = 0.784
(0.784 – So)/So = 0.02 => So = 0.784/1.02 = 0.7686
10. Today's Exchange Rates Monday, Feb 09,2009
Code
Country
Units/USD USD/Unit
Units/CAD
CAD/Unit
ARP
Argentina (Peso)
0.9999
1.0001
0.6447
1.5510
AUD
Australia (Dollar)
1.9618
0.5097
1.2650
0.7905
ATS
Austria (Schilling)
14.7921
0.0676
9.5383
0.1048
1) What is the cross rate, ATS/ARP?
2) If AUD was expected to appreciates from 2/09/2009 to 2/09/2010 by 2% against US$, what
is the expected US$/AUD of 2/09/2010?
=> 1) ATS/ARP = (ATS/$)*($/APR) = 14.7921*1.0001 = 14.79358 (instead of 1.0001, you can
use 1/0.9999)
2) ($) price of AUD is 0.5097 on 2/09/2009 and it is expected to appreciate 2%
=> 0.5097*(1.02) = 0.519894 (Of course, you can use (S1-So)/So=0.02 with
So=0.5097. However, this problem is a lot simpler than that.)
11. A MNC has the following cash flows from their operations around the world. What is the $
amount of total cash flows from all the operations?
US operation: $100m, Canadian operation: C$150m, Japanese operation: 12 billion yen, UK
operation: 70m pounds
USD/CAD 0.78401, USD/GBP 1.8102, USD/JPY 0.0089682
If all the FC values increase 10% against the US$, what would be the new $ amount?
=> 100m + 150m*0.78401 + 12,000m*0.0089682 + 70m*1.8102 = $451,933,900
If all the FC values increase 10%, then the new exchange rates are
0.78401*1.1, 0.0089682*1.1, 1.8102*1.1. Therefore, 100m + [150m*0.78401 +
12,000m*0.0089682 + 70m*1.8102]*1.1 = $487,127,300
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12. You have just sold a share of XX French firm, for e50. The exchange rate is $ 1.25/e now
and it was $1.15/e a year ago. You did receive 2 euro dividend for each share while holding this
stock. Compute the euro price of the stock a year ago if the $ rate of return from this investment
is 30%?
=> From the sale of one share of the company stock, you have 50 euro. At the current exchange
rate of $1.25/e, you can get 50*1.25=$62.50. You also have received 2 euro dividend for each
share, which is equal to 2*1.25=$2.50. Altogether, you have just received $65.00 from investing
in just one share. 30% dollar rate of return implies that = ($Ending Balance - $Beginning
Balance)/$ Beginning Balance = (65 – Beg)/Beg = 0.30 => $Beg Balance = $65/1.3 = $50. In
other words, you have started with $50 to begin with. Since the exchange rate at that time was
$1.15/e, the euro price of the stock share is e50*(1/1.15) = e 43.48.
Alternatively, you can use euro appreciation rate (against $) and the foreign currency
(euro) rate of return on this stock. Euro currency appreciation (against $) = (S1 – So)/So = (1.25
– 1.15)/1.15 = 0.087 or 8.7% appreciation. Euro rate of return on this stock = (50 – Po + 2)/Po.
The 1 + $ rate of return is a combination of these two returns or 1 + R$ = (1 + euro appreciation
rate)*(1 + euro rate of return on this stock) => 1.3 = (1.087)*(1 + euro rate of return on this
stock) => euro rate of return on this stock = 1.3/1.087 -1 = 0.196 or 19.6%. Now, the euro rate
of return on this stock = (50 – Po + 2)/Po = 0.196 => Po = 52/1.196= e43.38
Chapter 2: International Monetary System
1. What is the major problem with the Bimetallism? How to save such a monetary
system? What is the major problem with the Gold exchange standard? How could you have
saved that system? What is the price-specie-flow mechanism?
=> The major problem with Bimetallism is that “Bad money drive good money out
of circulation”, Gresham’s law. The government fixed the exchange rate as 1ounce Gold
= 16ounce Silver. Such monetary system can be saved by letting the market determine the
exchange rate between gold and silver.
The major problem with the Gold exchange standard is that only $ is fully convertible to gold,
and as more $ is provided to the world, as result its value drops. This system can be saved by
reducing the $ printed.
The Price-Specie-Flow mechanism is when automatically, a balance of trade can be achieved as
the gold flows between countries.
2. Explain: 1) Price-Specie-Flow 2) Snake
=> 1) Price-Specie-Flow:The price-specie-flow is a part of the classical gold exchange. It
represents the automatic restoration of international payments to balance. When there is a
temporary trade surplus/deficit, the country with the trade surplus (exported more) has more gold
4
from payments. Therefore the country with the trade deficit (exported less) has less gold from
payments. Therefore the prices in the country with the trade deficit decrease because the people
have a lack of gold. With this decrease in price, the country with the trade surplus spends their
gold on exports from the country with the trade deficit because of the lower prices. Therefore the
country which had the trade deficit (and less gold) gets gold and the trade balance is returned.
2) Snake is part of the target-zone. The target-zone was set by the European Monetary System.
They set-up the European Currency Unit. This was to regulate the exchange rate of the currency
and keep it in the target zone within a change of 2.25% up or down. If the currency got out of the
target zone it would be regulated (supply) to return it to the target zone. In 1990 the change in the
target zone was lowered to 1.125% and the European currencies moved together like a snake.
Eventually moved 0% and Euro came in.
2. Differentiate between the classical gold standard and gold exchange rate systems
=> The Classical Gold std was between 1875-1914. All currencies were fully convertible into
gold. Under this system the supply of money is solely dependent on the amount of gold the
economy/ country has.
Advantage: $ supply is under tighter control & keeps the value of money.
Disadvantage: could create a shortage of $ as the economy grows
The Gold-Exchange (the Bretton Woods System, IMF System) took place between 1945-1972,
fixing the dollar value of gold at $35/ounce. Only US$ can be fully converted into gold. Other
currencies are fixed to us $. The system is based on the $ maintaining it value, however, as more
$ was provided to the world, $ value dropped.
Chapter 2-1: Exchange Rate Determination
1. Describe how the changes in the following macroeconomic variables effect the exchange
rates? (provide logical rationale and use diagrams)
a) higher inflation in UK (BP)
b) higher interest rate in Germany & higher inflation in the US (euro)
c) Comment on the statement, “a stronger economy has a stronger currency” Is that true? Why
and why not?
=> a) prices of goods and services in UK increase => demand for UK products decreases =>
demand for BPs decreases => ($) price of BP (we call it an exchange rate) decreases (=> stronger
$ and weaker BP). You need to show a shift of demand for BP to the left.
b) First, higher interest rate in Germany => increased investments in Germany to get a higher
return on investment => demand for euro increases => ($) price of euro (called an exchange
rate) increases (=> stronger euro and weaker $). You need to show a shift of demand for euro to
the right. Second, a higher inflation in the US (we did this in class) - - => higher exchange rate.
Since both factors move the exchange rate up, the exchange rate increases.
c) Yes, a stronger economy tends to have a stronger currency. Stronger economy can have an
impact on the exchange rate in two different ways; one is through a consumption channel and the
5
other is an investment channel. It may depend on which side has stronger impact on the
exchange rate. However, “a stronger economy has a stronger currency” is empirically true
because the investment side has been dominating the consumption side empirically.
Let’s say Germany has stronger economy
(i) Consumption Side
→ German income increases
→ Demand for U.S. products (as well as German products) increases
→ Demand for US$ increases = Supply of € increases
→ € supply curve shifts out
→ ($) price of € (called an exchange rate) decreases
→ Stronger $ and weaker €
(ii) Investment Side
→ Investment in Germany increases to get a higher return from the stronger German Economy
→ Demand for € increases
→ Demand curve for € shifts out
→ ($) price of € (called an exchange rate) increases
→ Stronger € and weaker $
Empirically, investment side dominates. Strong economy results in the stronger currency
$/€
$/€
S (€)
S (€)
S1
S0
D (€ )
S1
S0
D’ (€)
D’ (€)
D (€ )
Q (€)
(i) Consumption Side
Q (€)
(ii) Investment Side
2. Explain how changes in the following macroeconomic variables affect exchange rates.
a) Higher UK inflation rate & Higher US interest rate.
b) Higher UK interest rates & Stronger US economy
=> a) Higher UK inflation => UK products become more expansive => demand for UK products
decreases => demand for BP decreases => ($) price of BP=exchange rate decreases, Higher US
interest rate=> increased investments in the US for a higher return=> demand for $=supply of
BP increases=> ($) price of BP decreases=exchange rate decreases. Both of these two forces
move the exchange rate in the same direction, lower exchange
rates.
6
b) Higher UK interest rate=> increased investments in the UK=> demand for BP increases=>
($) price of BP increases =exchange rate increases. Stronger US economy can have an impact
on the exchange rate in two different channels, one is through a consumption channel and the
other is an investment channel. Investment channel is the dominant choice.
3. “An increase in the US interest rate would result in an influx of foreign capital as everyone
wants to invest in the US for a higher return. The demand for US$ will increase as a result. The
demand for $ is the same as the supply of a foreign currency. An increase in the supply of a
foreign currency would decrease the $ price of a foreign currency, which is the exchange rate. A
decrease in the exchange rate would, however, causes an increase in the demand for the foreign
currency, causing the foreign currency to be stronger and the US$ weaker. The conclusion is that
an increase in the US interest rate would result in weaker US$.”
=> Increase US interest rates
 Increase investment from foreign countries at higher return
 Demand for US$ increases (demand shift right), supply of FC decreases
 $ price of FC (exchange rate) decreases ($ gets stronger) (FC gets weaker)
The statement has gone too far. The real things that happen are shown above. The demand shifts
right. The supply for FC will be lower. And simple laws of supply and demand display higher
exchange rate. The $ gets stronger and new equilibrium is higher.
Chapter 3: Balance of Payments
1. Differentiate between portfolio investment and foreign direct investment
=> Portfolio investment is seeking a higher return and a greater reduction in risk through a
portfolio diversification. FDI is trying to secure a controlling interest of the business and run the
business.
2. What is J curve?
=> It takes time to see an improvement in trade balance as the domestic currency value gets
lowered. Initially, the trade balance gets worsened until the exchange rate change has an impact
on the consumption and production of the economy. It is like our spending on oil. When the
price of oil goes up, we spend more money on oil (increased price x quantity used) until the
consumption of decreases substantially in response to increased price.
3. What is SDR?
=> Official currency created by IMF.
4. Define the balance of payments
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=> The statistical record of a country’s international transactions over a certain period of time
presented in the form of double-entry bookkeeping
Chapter 5: Foreign Exchange Market
1. Suppose that you collect the following quotes from foreign exchange traders:
London: euro/£ = 1.9
New York: £/$ = .5
Frankfurt: euro/$ = 0.9
You recognize that there is an arbitrage opportunity here. What sequence of trades will allow
you to profit from this opportunity? You start with one million dollar investment, and show that
there exists an arbitrage opportunity, which also suggests the sequence of trades. (Determine
High and Low!)
 Trying to have $/BP rates:
$/BP = 2 in New York, another $/BP = ($/euro)*(euro/BP)=(1/.9)*1.9 = 2.11
Therefore, Buy BPs Low in NY and Sell BPs High in L & F
1) Buy BPs in NY using $1m, $1m * .5 (BP/$) = 500,000 BPs
2) Sell BPs for euro in London, 500,000 BPs * 1.9 (euro/BP) = 950,000 euro
3) Sell 950,000 Euros for $s in Frankfurt 950,000 euro * (1/.9) ($/euro) = $1,055,555.56
The arbitrage profit = $55,555.56
2. Suppose that you collect the following quotes from foreign exchange traders:
London: euro/£ = 1.9
New York: £/$ = .5
Frankfurt: $/euro = 1.1
You recognize that there is an arbitrage opportunity here. What sequence of trades will allow
you to profit from this opportunity? You start with one thousand dollar investment, and show
that there exists an arbitrage opportunity, which also suggests the sequence of trades. (That is,
determine High and Low!)
=>: Use BP as the foreign currency, $/BP = 1/.5 = 2 in NY
Another $/BP = ($/euro)*(euro/BP) = 1.1 * 1.9 = 2.09 in L and F
Now, Buy Low BPs from NY and Sell High BPs in L and F
1) Buy BPs using $1000 in NY: you can have 500 BPs $1000*1/$2 per BP = 500BPs
2) Sell 500 BPs for euro in London: you can have 950 Euros 500BP*1.9euros = 950 Euros
3) Sell 950 Euros for $s in Frankfurt: you can have $1045 950euros*1.1$/euro = $1045,
$1,045 - $1,000 = $45
=> $45 arbitrage profit
3. a) American quotes of euro are $1.149425 in Paris and $1.09577 in NYC. Show how you can
make an arbitrage profit with $1,000 investment.
b) European quotes of euro and SF are euro 0.87/USS and SF1.17/US$ respectively. And, the
direct market quote between euro and SF is euro 0.78/SF. Show how you can make a triangular
8
arbitrage profit with $1,000 investment. (Show that an arbitrage opportunity exists, identity
H&L)
=> a) $/euro=1.149425 in Paris $/euro=1.09577 in NYC => Sell High in Paris and Buy Low
in NYC : $1,000 => 912.6 Euros => $1,048.97 arbitrage profit=$48.97
b) Choose between euro and SF to determine the American term exchange rates to compare
and determine High and Low. If we choose euro, then we need to have $/euro at two
different locations. $/euro = 1/.87 = 1.149425. Another $/euro = ($/SF)*(SF/euro) =
(1/1.17)*(1/0.78) = 1.09577. Now, we can determine High and Low (note that
these numbers are the same as in 1). $1,000 => 1,170 SFs => 912.6 Euros => $1,048.97.
(If you choose SF, then $/SF=0.85 vs. $/SF=($/euro)*(euro/SF)=(1/0.87)*(0.78)=0.897)
4. Suppose that you collect the following quotes from foreign exchange traders:
London: C$/£ = 2.5 (2.5 C$s for 1 BP)
New York: £/$ = .5-.6 (bid-ask prices)
Frankfurt: C$/$ = 1.2
Is there an arbitrage opportunity? Please show how you can or cannot make arbitrage profits
with $1,000 investment. You need to note High & Low where necessary.
=> Choose a FC to use from C$ and BP. Either choice should produce the same
result. Let’s do it with BP. Then, you have $/BP=1/0.6~1/0.5=1.667~2.0 in
NY, $/BP=($/C$)*(C$/BP)=(1/1.2)*(2.5)=2.083. The average of bid-ask rates in
NY=1.8335, less than $/BP in London & Frankfurt. => Now, we have Low in NY and
High in L&F. Buy BP in NY, then Sell BP for C$ in London (only place where C$ and
BP are traded), then Sell C$ for $s.
1. Buy BP using $1000 in NY at $/BP=2.0 since you need to pay more when you buy
and get paid less when you sell => $1000*(1/2)=BP500
2. Buy C$ using BP500 at C$/BP=2.5 in London=>BP500*2.5=C$1250
3. Sell C$1250 for $s at C$/$=1.2 in Frankfurt=>C$1250*(1/1.2) = $1041.67
4. The arbitrage profit is $41.67
5. A US firm sells plug trays to England with a payment of one million BPs due in 90 days. The
current spot rate is $1.42/BP and the 3 month forward rate is $1.43/BP. You are considering two
alternatives to sell one million BPs upon receiving the A/R payment. You can use a forward
contract to sell the money in 3 months. Alternatively, you will be selling BPs at the prevailing
future spot rate. The $/BP rate is expected to be as high as 1.50 with 70% probability and as low
as 1.30 with 30% probability. 1) What is the expected exchange rate based on the information
given? 2) Determine the estimated $ receipt from the sale of BPs in two alternative
arrangements. 3) If you do not mind taking an exchange rate risk as long as you receive at least
$5,000 more from taking the risk, which alternative looks better? 4) What kinds of options (call
or put) would you consider using? What is the advantage of having an option?
=> A/R of 1 million BPs in 90 days
1) .7*1.50 + .3*1.3 = 1.44
2) Forward contract: $1.43m, Expected $ receipt from selling 1m BPs at the future spot rate
= $1.44m.
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3) You would take future spot market transaction since you expect to make additional $10k
from it. Of course, the actual amount will be either $1.5m or $1.3m.
4) Put because it is accounts receivable.
6. A US firm buys plug trays from England with a payment of one million BPs due in 90
days. The current spot rate is $1.45/BP and the 3 month forward rate is $1.43/BP. You are
considering two alternatives to buy one million BPs for the A/P. You can use a forward contract
to secure the money in 3 months. Alternatively, you will be buying BPs at the prevailing future
spot rate. The $/BP rate is expected to be as high as 1.60 with 70% probability and as low as
1.30 with 20% probability. There is small 10% chance that the rate could be $1.4/BP. 1) What is
the expected exchange rate based on the information given? 2) Determine the estimated $ cost to
secure BPs in two alternative arrangements. 3) Which strategy do you like better and why? You
were told that that you can avoid the exchange rate risk by purchasing the BPs today. Do you
think it is a good idea? Why or why not?
=> 1) E(S1) =.7*1.60+.2*1.30 +.1*1.40 = $1.52/BP
2) Fwd: $1.43 * 1 mil= $1.43m, Future Spot:$1.52*1 mil= $1.52m
3) I like the forward strategy $1.43/BP better, since the amount is smaller and certain,
than the expected rate of $1.52/BP.
7. Explain what are the factors determining the size of spread. How do they affect the spread
size?
=>Factors determining the size of spread:
- Trading volume increase→ Spread gets smaller
- Trading frequency increase → Spread gets smaller
- Volatility of exchange rate increase →Spread gets bigger (greater risk)
8. A US firm is buying plug trays from England with a payment of one million BPs due in 90
days. The present exchange rate is So=$1.71/BP and the future spot rate (S1) is expected to be
as high as $2/BP or as low as $1.6/BP. F=$1.73/BP. Probability Distribution: S1=$2/BP with
30% Prob, and $1.6/BP with 70% Prob. The exercise exchange rate of the option is $1.72/BP
with a premium of $0.01/BP. The US and UK interest rate are respectively 10% and 6%
per annum. Discuss three different ways (sell at S1, Sell forward, Making a pound deposit today,
Options) to deal with 1 million pound A/P and characterize their advantages and disadvantages.
=> Objective: minimizing $ cost of securing one million
pounds. E(S1)=0.3*2+0.7*1.6=$1.72/BP. UH: $1.72m FV, Uncertain, FH: $1.73m FV,
Certain, MMH: Deposit PV of 1m BPs=1,000,000*(1/1.015)=985221.67 BPs. To secure
this amount of BPs today, you need to spend $1,684,729.07 PV, Certain. FV of
MMH=1,684,729.07*1.025 =$1,726,847.29 FV, Certain. Call Options: The maximum amount
to spend to secure 1m BPs is $1.73m including the premium paid. You may spend less than that
to buy 1m BPs when S1 < K. FV, maximum in case S1>K. Since FV of MMH is less than FH,
FH is out of the consideration. If you think that the difference between $1.72m UH is much less
10
than $1,726,847.29, you may consider taking UH even if it is just an estimate and risky. Call
options places a ceiling and you may be able to save (sometimes, save quite a lot) as your worst
case is covered.
9. What is the forward premium rate (annualized) when 1 C$ in US$ = 0.7840 today, and 60 day
Fwd = 0.7843?
=> (0.7843 -0.7840)/0.7840 * 360/60 = 0.002296 or 0.2296%
Chapter 6: Parity Conditions and Currency Forecasting
1.If the interest rate in the US is 5% and the UK interest rate is 4%, how much arbitrage gain do
you expect from $1,000 investment?
=> Since the US rate is a $ rate and the UK rate is BP rate, we need current and future
exchange rates (or forward rate) to be able to determine whether we have an arbitrage
opportunity and how much.
2. If BOA (Bank of America) interest rate is 4% and NB (Nations Bank) rate is 5%, show that
you can make arbitrage profits with $1,000 Borrowed Low and Invest (=deposit) High. Use cash
flows at time 0 and 1. Assume that the rates offered by each bank are the same for both lending
and deposit.
=> You have to borrow low from BOA 1,000*(1+0.04)= 1,040;
and invest high in NB 1,000*(1+0.05)= 1,050.
The arbitrage profit will be $10= 1,050-1,040
3. If actual lending and deposit rates offered from each bank are 0.6% different from its reference
rates given above (i.e., BOA has 3.4% for deposit and 4.6% for its loan. Likewise, Nations has
4.4% and 5.6%). Is there an arbitrage opportunity? Show that the arbitrage does/doesn’t work
with the profit/loss.
=> Consideration: borrow low from BOA at 4.6% → $-1,046
invest high in NB at 4.4%→ $+1,044. If the current situation is considered there will be
a lost. No arbitrage opportunity.
4. Given the information given: 6 month US interest rate: 6% per annum, 6 month Swiss interest
rate: 8% per annum, current exchange rate: $0.78/SF, is there an arbitrage opportunity if the
actual market forward rate is $0.79/SF ~ $0.81/SF? If so, how can you make an arbitrage profits
and determine the size of the profit if you can borrow $1000 or equivalent amount in SFs.
=> US interest 6%/2= 3% Swiss Interest Rate 8%/2=4%
Since we have a current exchange rate of $0.78/SF and Average expected exchange rate
of (0.79+0.81)/2= $0.80/SF.
LHS= (1+i$)= 1.03 →Low & RHS= (1/So)*(1+iSF)*F=(1/0.78)*(1.04)*0.80=1.067
Thus you have to borrow low from the U.S. at 3% →-1,030
And invest in Swiss $1,000*(1/0.78)= SF1,282→invest in Swiss at 4% →(1,282*1.04)=
SF1,333.3333 → Convert SF to $, SF1,333.3333*(1/0.79)= $1,053. 33
As result the arbitrage profit is ($1,053.33-1,030)= $23.33
11
5. a) If actual lending and deposit rates offered from BOA and Nations bank are such that BOA
has 3.6% for deposit and 4.4% for its loan and Nations has 4.6% and 5.4%. Is there an arbitrage
opportunity? Show that the arbitrage does/doesn't work with the profit/loss.
b) Determine the implied forward rate using the information given below: 6 month US inter rate:
8% per annum, 6 month Swiss interest rate: 6% per annum Current exchange rate: $ 0.73/SF, If
the actual market forward rate is S0.93/SF, is there an arbitrage opportunity? If so, how can you
make an arbitrage profits and determine the size of the profit if you can borrow $1000 or
equivalent amount in SFs.
=> a) Yes, there is an arbitrage opportunity.
Borrow low from BOA at 4.4% loan rate → -1,044
Invest high in NB at 4.6% deposit rate → +1,046
The arbitrage profit will be $2.00
b) (1+i$) = (1/So)*(1+iSF)*F →1.04 = (1/0.73)*(1.03)F → F= 0.74
Since actual FWD rate ($0.93/SF) > implied FWD rate ($0.74/SF) → you have to
borrow from US and invest in Swiss.
1)Borrow from US at 4% (8%/2) →-1,040.00
2) Invest in Swiss at 3% (6%/2)
$ 1,000* (1/0.73) = SF 1,369.86→ SF 1,369.86*1.03 = SF1,410.96(invest return)
→ convert SF to $: SF 1,410.96*($0.93/SF)= $1,312.19
The arbitrage profit is 272.19 = (1,312.19-1,040.00)
6. If the expected inflation rate in the US is 5% and the expected inflation rate in Swiss is 7%,
how much SF is expected to appreciate?
=> 5-7=-2% SF is expected to depreciate 2% against $.
7. What is the International Fisher Equation? What is the assumption made to get this equation
from the Domestic Fisher? If the US and UK inflation rates are expected to be 3% and 5%
respectively, how much the BP is expected to appreciate against the dollar? Explain theoretically
how you can come up with a relationship between nominal interest rate differential and
expected change in the exchange rate. If the US interest rate is 5%, what is the UK interest when
the International Fisher assumption is satisfied? What is your expected change in the BP value
relative to US$ based on the interest rate differential?
=> The International Fisher Equation: E(e)= E(I$)- E(I£)= i$-i£, which use the relative PPP
formula E(I$)- E(I£) = E(S1-So)/So & E(e) = E(I$)- E(I£). The assumption is that real
interest rates are equal across countries; the nominal interest differential should be equal
to the expected inflation differential, which should be equal to the change in the exchange
rate.
I$= 3% and I£= 5% → E(e) = 3% -5%, BP is expected to appreciate at -2% (or
depreciate by 2%)
Theoretical relationship between nominal interest rate differential and expected
change in the exchange rate: 1) the nominal interest rate differential is represented by
the difference between two countries interest rate, on the other side 2) the change in
the expected exchange rate is represented by the difference between two
countries inflation. 3) From there we result in the nominal interest differential equal to
the change in the expected exchange rate is represented.
12
If i$= 5% →E(I$) – E(I£)= i$- i£ →3-5=5-x →-x=-7 → i£= 7%
The expected change in BP value is 2% appreciation.
8. 1) How is the relative PPP different from the absolute PPP? According to the relative PPP,
what is causing the exchange rate to change? If the US and UK inflation rates are expected to be
5% and 3% respectively, how much the BP is expected to appreciate against the dollar? Does it
make sense?
2) What is the significance of combining the relative PPP and International Fisher?
=>1) Absolute PPP hold that change in interest rate come from change in Price
(products), whereas Relative PPP hold that change in nominal interest rate
differential come from interest rate change.
According to the relative PPP, it is the inflation rate that causes the exchange rate
to change. I$= 5% I£= 3% → E(e) = 5%-3% BP is expected to appreciate at 2%
2) Relative PPP: e=IA-IB, in terms of projected changes, we can have E(e) = E(IA) – E(IB.).
On the other hand, International Fisher: iA – iB = E(IA) – E(IB)
Combining both equations (see E(IA) – E(IB) are present in both equations), we can say that E(e)
= iA – iB
The significance of E(e) = iA – iB equation instead of E(e) = E(IA) – E(IB.) equation is that we
can use actual (nominal) interest rates (e.g., US and UK T bill rates) which can be obtained from
current financial information sources like WSJ, finance.yahoo.com, etc from the combined
equation. For relative PPP, we need to estimate future inflation rates to determine how much the
exchange rate (foreign currency value) is expected to change. Making a projection of future
variable (here inflation rate) is difficult and arbitrary.
9. What is the expected exchange rate of US$/C$, given the probability distribution as below?
US$/C$ Probability
0.96
50%
0.83
40%
0.75
10%
What is the forward supposed to be according to the forward parity? With the benefit of
hindsight, we learned that the actual rate was US$1.03/C$. What is the %forecasting error in this
case?
=> E(S1)=.5*0.96+.4*0.83+.1*0.75=0.887
F = E(S1) according to the forward parity, so F=0.887 as well.
%Forecasting error = (1.03-0.887)/1.03 = > 13.88%
10. What are four major parity conditions? Provide detailed explanations to all four parity
conditions including the assumptions needed, equations, empirical findings (working well in
reality?), and relationships between them.
=> 1. CIRP: From the no arbitrage condition:
One $ invested anywhere in the world should yield the same $ rate of return
-three assumptions:
1) the same risk
2) no transaction costs
3) no restrictions on foreign investments including no or identical taxes
13
2. PPP:
purchasing power parity : One $ (or one BP) should have the same purchasing
power around the world.
- absolute version: P$= So*P£ or So = P$/P£
- relative version: (S1-So)/So= i$ -i£ or e = i$ – i£
Three assumptions:
1) identical consumption patterns across the border
2) no transportation costs,
3) all goods are tradable
3. The Fisher Effect
1) The Fisher Effect (closed or domestic version) the nominal interest rate is equal to a real
interest rate plus an expected rate of inflation. I$ = ρ$ + E(I$)
2) The Fisher Open (or The International Fisher Effect)
i$ = ρ$ + E(I$)
i£ = ρ£ + E(I£)
Assuming that the real interest rates are equal across countries (ρ$ = ρ£), the nominal interest
differential should be equal to the expected inflation differential, which again should equal
the change in the exchange rate according to the relative PPP. That is, E(e) = i$ – i£ is from
the combination of the relative PPP and the International Fisher. The significance of this is
that we can get the interest rate more easily, while the data on expected inflation data is hard
to obtain.
4. Forward Parity:
The forward differential equals the expected change in the exchange rate or, the forward rate is
an unbiased predictor of the future spot exchange rate, F = E(S1) or (F-So)/So = E(e)
o
Combination possible: 1) Forward Parity & the Relative PPP
2) Fisher international & the Relative PPP
11. Given the following information, determine the forecasting error using the formula,
(|F-R|/R).
Which forecast between the British pound and the Mexican peso is more accurate? (Hint:
F=forecast, A=actual, realized).
F = $1.8/£,A = $2.0/£
F = $ 0.095/MP, A = S0.10/MP
=>Forecasting error= |F-R|/R
British Pound
Mexican Peso
|F-R|/R = |1.8-2.0|/2 |F-R|/R = |0.095-0.10|/0.10
= 0.10
= 0.05
Results: The Mexican Peso forecast is more accurate with a forecasting error of 0.5%,
compared to 1% for the British Pound forecasting error.
12. . Given the information given below:
6 month US interest rate: 2% per annum, 6 month Swiss interest rate: 6% per annum
14
Current exchange rate: $0.78/SF ~ $0.80/SF
Using the average of bid-asked prices, determine the implied forward rate. If the actual market
forward rate is $0.80/SF ~ $0.82/SF, is there an arbitrage opportunity? Can you determine the
directions of “borrow low and invest high” by comparing the implied forward rate and the
average of the actual forward bid-asked rates? How? Can you determine whether there is an
arbitrage gain or not by comparing the implied forward rate and the actual bid-asked rates?
How? If there is an arbitrage opportunity indeed, how can you make an arbitrage profits and
determine the size of the profit if you can borrow $1000 or equivalent amount in SFs.

i$ 6mo = 2% APR
i£ 6mo = 6% APR
S0 bid = $0.78/SF,
S0 asked = $0.80/SF => S0 AVG = $0.79/SF
F6mo bid = $0.80/SF, F6mo asked = $0.82/SF => F6mo AVG = $0.81/SF
Implied F
𝟏
𝑪𝑰𝑹𝑷 𝑬𝒒𝒖𝒂𝒕𝒊𝒐𝒏: 𝟏 + 𝒊𝒖𝒔 =
× (𝟏 + 𝒊𝑺𝑭 ) × 𝑭
𝑺𝟎
(1 + 0.02/2) = (1/0.79)*(1 + 0.06/2)*F
F6mo = [(1 + 0.01)*0.79]/( 1 + 0.03) = $0.7747/SF
Arbitrage Opportunity
LHS =(1 + 0.02/2) vs RHS= (1/0.79)*(1 + 0.06/2)*(0.81)
1.01 < 1.0567
L
H
Arbitrage opportunity may exist. If it does indeed exist, then you want to borrow Low from
the US and Invest High in Swiss for 6 months.
Can we determine High and Low (the Arbitrage trading directions) by comparing
Implied F vs. AVG Actual F? Yes
The implied forward rate obtained $0.7747 is less than the average of actual forward rates
$0.8100. Since CIRP holds (RHS is equal to LHS=1.01) when the implied forward rate is
imputed. As the average of actual forward rates ((bid+asked)/2) is greater than the implied,
we know that the RHS with a forward rate higher than the implied ought to be greater than
LHS, suggesting that the arbitrage trading should be borrow low from the US and invest high
in Switzerland to produce arbitrage gains, if any.
Can we tell whether we will have Arbitrage Gains by comparing the Implied forward
rate and Actual Bid-Asked Forward Rates? Yes
Using the implied forward rate and the actual forward rates,
$0.7747/SF
<
$0.8000/SF ~$0.8200/SF
15
You realized that even the bid actual forward rate is higher than the implied forward rate,
indicating that there is a very strong likelihood that we can make arbitrage profits by
borrowing low in the U.S. and invest high in Swiss. The implied is clearly out of the range
even when we take into consideration the bid-asked transactions costs. The disparity between
implied and actual rates is so big that we will most likely to have a arbitrage gain.
Arbitrage Strategy
a. Borrow $1,000 in the U.S.
b. Convert $1,000 at S0 asked = $0.80/SF
$1,000 * SF(1/0.80)/$ = SF1,250
c. Invest SF1,250 in Swiss at i£ 6mo = 6% APR
SF1,250 * (1 + 0.06/2) = SF1,287.5
d. $ Revenue in 6 months at F6mo bid = $0.80/SF (selling SFs for US$s)
SF1,287.5 * $0.8 = $1,030
e. Debt at i$ 6mo = 2% APR
$1,000 * (1 + 0.02/2) = $1,010
f. Profit
π = $1,030 - $1,010 = $20
13. What is the expected exchange rate of US$/C$, given the probability distribution as below?
US$/C$ Probability
0.96
40%
0.83
50%
0.75
10%
What is the forward supposed to be according to the forward parity? With the benefit of
hindsight, we learned that the actual rate was US$1.03/C$. What is the %forecasting error in this
case?
=>Expected Exchange rate ($/C$)
$/C$
0.96
0.83
0.75
Probability
40%
50%
10%
$/C$ * Pi
0.384
0.415
0.075
0.874
E(S0) = $0.874/C$
Forward Rate according to the Forward Parity
Forward Parity: F = E(S0)
16
Therefore, according to the forward parity, forward rate should be $0.874/C$
Forecasting Error
S1 = $1.03/C$
𝑭𝒐𝒓𝒆𝒄𝒂𝒔𝒕𝒊𝒏𝒈 𝑬𝒓𝒓𝒐𝒓 =
=
|𝑭𝒐𝒓𝒆𝒄𝒂𝒔𝒕𝒆𝒅 𝑽𝒂𝒍𝒖𝒆 − 𝑹𝒆𝒂𝒍𝒊𝒛𝒆𝒅 𝑽𝒂𝒍𝒖𝒆|
𝑹𝒆𝒂𝒍𝒊𝒛𝒆𝒅 𝑽𝒂𝒍𝒖𝒆
|0.874 − 1.03|
= 15.15%
1.03
14. a) European quotes of euro are euro 0.87/US$ in Paris and euro 0.91/US$ in NYC. Show
how you can make an arbitrage profit with $1,000 investment.
b) European quotes of euro and SF are euro 0.87/US$ and SF1.17/US$ respectively. And, the
direct market quote between euro and SF is euro 0.78/SF. Show how you can make a triangular
arbitrage profit with $1,000 investment. (Show that an arbitrage opportunity exists, identity
H&L)
=>
14. a)
S0 = 1/0.87 = $1.1494/€ in Paris
High
S0 = 1/0.91 = $1.0989/€ in NYC
Low
π = $1,000 * (1.1494 - 1.0989) = $50.5
14. b)
Use € as the FC. Then you want to have two $/€ quotations at different locations.
One
S/€ = 1/0.87 = $1.1494/€
High
Another
$/€ = ($/SF)*(SF/€) = (1/1.17)*(1/0.78) = 1.096 Low
Starting with $1,000, you need to get SFs first. Then, sell SFs for euro. Finally, sell euro for $s.
a) Buy SF using $ at S0 = $0.8547/SF
$1,000 * (1/S0) = $1,000 * SF1.17/$ = SF1,170
b) Sell SF for €
SF1,170 * €0.78/SF = €912.6
c) Convert into $ to realize the $ profit
€912.6 * $1.1494/€ = $1,048.94
π = $1,048.94 - $1,000 = $48.94
15. a) The actual exchange rate in Frankfurt is different from the theoretical rate. You recognize that
there is an arbitrage opportunity here using the actual rate. The sequence of trades will start from
NY and allow you to profit approximately $41.67 with $1,000 investment. What is the actual
exchange
rate in Frankfurt?
The exchange
rate in NY
is
$1.63/euro.
b) European quotes of euro and SF are euro 0.87/US$ and SF1.17/US$ respectively. And, the
direct market quote between euro and SF is euro 0.78/SF. Show how you can make a triangular
arbitrage profit with $1,000 investment. (Show that an arbitrage opportunity exists, identity
H&L)
17
15. a)
S0 = $1.63/€ in NY
π = $1,000 * (S0 Frankfurt - 1.63) = $41.67,
S0 = $1.67167/€ in Frankfurt
15. b)
$/€:
S0 = 1/0.87 = $1.1494/€
$/SF: S0 = 1/1.17 = $0.8547/SF
€/SF: S0 € & SF = €0.78/SF
Use € as the FC. Then you want to have two $/€ quotations at different locations.
$/€:
1/0.87 = $1.1494/€
High
$/€:
($/SF)*(SF/€) = (1/1.17)*(1/0.78) = 1.096
Low
Starting with $1,000, you need to get SFs first. Then, sell SFs for euro. Finally, sell euro for $s.
a) Buy SF using $ at S0 = $0.8547/SF
$1,000 * (1/S0) = $1,000 * SF1.17/$ = SF1,170
b) Sell SF for €
SF1,170 * €0.78/SF = €912.6
c) Convert into $ to realize the $ profit
€912.6 * $1.1494/€ = $1,048.94
π = $1,048.94 - $1,000 = $48.94
16. Why does PPP fail to work in reality ? What about CIRP? What is the key assumption made
for International Fisher?
=>
PPP
PPP ($ CPI’s between two countries should be the same) doesn’t usually work in reality because
of its assumptions. Those assumptions are
1) Identical consumption patterns among countries
2) No transactions costs
3) All goods are tradable
CIRP
For the same reason, CIRP doesn’t hold due to the disparity between reality and assumptions.
Assumptions for CIRP are:
1) Same risk in investing in two different countries
2) No transaction costs
3) No restriction on foreign investments + no or identical taxes
Key Assumption for International Fisher
Real interest rates between two countries are same (i real A = i real B)
Chapter 7: Currency Derivatives
1. Differentiate between: Primary vs. derivative products
18
=> The value of a primary product is determined by its own cash flows, while the value
of a derivative product is dependent on the value of a primary product.
2. What are the differences between forward and futures (you may focus on “currency”)?
Provide your brief explanations.
=>The forward and future are conceptually the same with the differences shown in the
chart below.
Forward
Self-regulated
Contract can be made for any currency
Bid-asked spread
No margin
Customized Contractual agreement between
two parties
Delivery based on contract terms
Traded over the counter (OTC)
No daily settlements
Future
Regulated by Commodities Futures Trade
Commission
Available in a few major currencies
commission
Must satisfy margin requirements
Standardized
Delivery 3rd Weds. Of March, June, Sept., Dec.
Traded on futures exchange floor (CME,
SIMEX, etc)
Daily settlements (marking to market)
3. If the futures settlement rates have changed from the current $.623/SF, to $.627, $.634, $.612
then how would the daily gain have changed on a futures contract for three SF futures contracts
(one SF futures contract is for SF125,000) if you take a long position? What is your ending
balance, if your beginning balance is $4,972.50. Do you have a margin call on the last day? If
you do, what is the variation margin? What is the new balance if you add $700 more than the
variation margin required? If you do not get a margin call on the last day, what is the futures
price to get the margin call at 1.5%.
=> Note Long=(new price-old price)*(3*125000SF), Begin Balance: $4972.50
Day 1: ($.627/SF-$.623/SF)*(3*125000SF)=$1500+$4972.5= Ending Bal $6472.50
Day 2: ($.634/SF-$.627/SF)*(3*125000SF)=$2625+$6472.5= Ending Bal $9097.50
Day 3: ($.612/SF-$.634/SF)*(3*125000SF)=-$8250+$9097.5= Ending Bal $847.50
Yes there is a margin call on the last day.
($.612/SF)*($847.5/3*125000SF)=.00369<1.5%
Now, ($.612/SF)(3*125000SF)(.02)=$4590 is the margin needed to carry on
You would have to add at least $3742.50 to current margin.
The new balance would be $700+$4590= $5290
4. You took a short position in three contracts of SF futures (125,000 SFs for one contract) at
10am CST on 3/11 for 2009 March delivery at S.623/SF. What is the initial margin amount at a
2% initial margin? Given that you put down $200 more than the 2% initial margin requirement,
what is the ending balance of your account at the end of 3/11 if the settlement price of 3/11
is S.627/SF? What is your new margin ratio at the end of the day of 3/11? Do you get a margin
call, if the minimum maintenance margin,1.5%? If so, how much is the variation margin?
Assuming that you are going to add $300 more than the variation margin, if you get the margin
call, what would be the ending balance of 3/11? If the futures rate increases to S.629/SF on 3/12,
19
do you get a margin call? What is the variation margin? What will be the ending balance if you
add $300 more than the variation margin?
=> To satisfy the initial requirement of 2% of the $ value of the position, you need
to have at minimum $0.623/SR * 3 * 125,000 * 0.02 = $4,672.50. $200 more than
the minimum =$4,872.60. As the futures price increased to $0.627, you have a gain
of (0.623-0.627)*375,000 = -1,500 (or a loss of $1,500). The ending balance
becomes $3,372.50 and the margin ratio = 3,372.50/(.627*375,000) = 1.43%. Since you
are below 1.5%, you get a margin call. The variation margin = 0.2*0.627*375,000 –
3,372.50 = $1,330 and the new balance will be $3,372.50 (current balance)+$1,330
(VM)+$300 (extra added)=$5,002.50. Another future price increase in the following day
results in a gain of (0.627-0.629)*375,000=-750. The ending balance becomes $4,252.50
with a margin ratio of 1.8%. No margin call.
5. You are taking a short position in 3 contracts of C$ futures (contract size=100,000) at 10am
today at US$0.5080. Your margin account currently has a balance of $2,500. Is this enough to
take this position? If not, you are going to add more money to bring the balance equal to the
initial margin required (2% initial margin) plus extra $500. How much do you need to
add? Assume that today’s settlement price on a CME C$ futures contract is $0.5075 and the next
three days’ settlement prices are $0.5147, $0.5086, and $.5096. If you run into a margin call
situation (1.5% maintenance margin), determine the variation margin and add $500 plus the
VM. On the other hand, if your margin ratio exceeds 2.4%, you are going to withdraw money
from your account to reduce your margin ratio back to 2%. Calculate the changes in margin
account due to price changes, the balance of the account and the margin ratio at the end of each
day before and after any additional adjustments in the account (VM and other
additions/withdrawals to/from the account).
=> The 2% initial margin amount should be 0.02*0.5080*3*100,000=3,048,
Since 2,500<3,048, you need to add more money. The initial balance is,
then, 3,048+500=3,548. The amount to be added is 3,548 – 2,500=1,048. The daily gain
(short- position) based on the settlement prices are: (0.5080-0.5075)*300,000=150,
(0.5075- 0.5147)*300,000=-2160, (0.5147-0.5086)=1830, (0.5086-0.5096)*300,000=300. The resulting balance of the first day is: 3,548+150=3,698. While you don’t have to
worry about the maintenance margin ratio of 1.5% since the balance has increased, you
may need to check whether the margin ratio exceeds 2.4%. The margin ratio
is 3,698/(0.5075*300,000)=0.024289 or 2.43%. Since the margin ratio at this point
exceeds 2.4%, you need to withdraw the margin to reduce the margin ratio back to 2%
level or 0.02*0.5075*300,000=3,045. In other words, you need to withdraw 36983045=$653. On the 2nd day, the ending balance becomes $3045-2160=$885 and the
margin ratio becomes 885/(0.5147*300,000)=0.00573 or 0.573% much less than the
1.5% maintenance margin level. VM=2% level – current balance=0.02*0.5147*300,000
– 885=$2,203.20. The resulting balance will be $885+$2203.20+$500=$3,588.20. On
the 3rd day, the balance will become $3,588.20+$1,830=$5,418.20. The margin ratio
will be obviously greater than 2.4% (you need to check!) and you need to withdraw
5,418.20 – 0.02*5086*300000=$2,366.60 and the balance after this withdrawal
becomes $3,051.60. The 4th day balance will become $3,051.60-300=$2,751.60. This
small loss does not seem to cause a margin call.
20
6. A US firm buys plug trays from England with a payment of one million BPs due in 90
days. The current spot rate is $1.42/BP and the 3 month forward rate is $1.415/BP. You are
considering two alternatives to buy one million BPs. You can use a forward contract to buy the
money in 3 months. Alternatively, you can use BP options to buy one million BPs at K=
$1.417/BP. Each BP option contract is written on 31,250 BPs and the current option premium is
$0.005/BP.
a) Which type of option the firm needs to buy, calls or puts?
b) How many option contracts does the firm need?
c) What is the total option premium?
d) If the future spot rate becomes $1.43/BP, are you going to exercise the options? Why?
e) With the benefit of hindsight, which alternative (between the forward and the options) turns
out to be a better choice? Why?
f) If you had the hindsight, do you think you would have purchased the options?
=> a) Call options as they need to secure (buy) one million BPs.
b) 1,000,000/(62,500/2)=1,000,000/31,250=32 contracts
c) 1,000,000*.005=$5,000
d) Since K=1.417 < S1=1.43, you want to exercise the call options and buy 1 million
BPs at a lower price(=exchange rate).
e) Since the forward rate=1.415 is less than K+pm=1.417+.005=1.422 and S1 > K,
the forward is a better choice with the benefit of hindsight.
f) No, the forward contract turns out to be the best one.
7. Given the currency rates below, determine the three-month forward bid-asked outright quotation rates
and the forward premium APR rates.
Spot $/BP 1.9712 – 1.9717
Three-month 57-54
S0($/£): 1.9712 – 1.9717
3-month: 57 – 54
Since the first number is greater than the second number, the forward rates are at a discount.
For Bid, 1.9712 – 0.0057 = 1.9655
For Asked, 1.9717 – 0.0054 = 1.9663
For Bid, [(F – S0)/S0] * [360/90] = [(1.9655 - 1.9712)/1.9712] * [360/90] = -0.0115
= -1.15%
For Asked, [(F – S0)/S0] * [360/90] = [(1.9663 - 1.9717)/1.9717] * [360/90] = -0.0109
= -1.09%
Chapter 8: Managing Transaction Exposure
1. Towson Company has exported machinery worth M$500,000 to a Malaysian manufacturing
company. The sale would be denominated in M$ on a one-year open account basis. The
opportunity cost of funds for Towson Company is 10%. The current spot rate is M$ 2/US$, and
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the forward M$ sells at a 10% discount. The finance staff of Towson Company forecasts that
the M$ will drop to 8% over the next year. Towson Company faces the following alternatives.
a) Don’t do anything, but wait one year to receive M$500,000.
b) Sell the M$ amount forward today.
c) Borrow M$ from Public Bank Berhad in Kuala Lumpur at 15% APR for the expected
future payment of M$.
d) Which alternative among three (a, b, c) seems to be most attractive and why?
=> So=1/2=$0.5/M$, M$ is expected to drop 8% => E(S1)=0.46, Forward M$ sells at
a 10% discount=> F=0.5*(1-0.1)=0.45. The objective of A/R is to maximize the $
receipt from the sale of M$500,000.
a) UH: expected to receive 500,000*0.46 = $230,000 FV, Uncertain.
b) FH: $225,000 FV, Certain.
c) MMH: Borrow PV of M$500,000 = M$500,000*(1/1.15) = M$434,782.61, Convert to
$s=434,782.61*0.5=$217,391.30 PV, Certain. To compare, it is better to have a FV of
MMH=$217,391.30*1.1=$239,130.44 FV, Certain.
d) MMH seems to be the best as it has the largest $ amount with certainty.
2. Tay Enterprises has just sold merchandise for 250,000 euro to a customer in Germany, with
payment due in euro three months from today. Tay Enterprises can borrow for three months from
a bank in Los Angeles at 6% per annum, or from a bank in Germany at 8% per annum. Today's
spot rate (direct basis) is $1.004/e. Three-month option contracts are available with
the following characteristics.
Contract size: 62,500 euro
Strike price: $1.005/e
Option premium, per option: $200
a) Assume that you in fact hedged the transaction by option contracts. On the day the option
matures, three months from now, the spot exchange is $1.005/e. Would you exercise the option
at that time or sell euro in the spot market? Why, and what is the dollar advantage of one choice
over the other?
b) What would have been your dollar sales proceeds, three months hence, if you had hedged via
the money market?
c) Given today's interest rates, what should be the three-month forward exchange rate for euro?
d) Given this forward exchange rate, what would have been your dollar sales proceeds had you
hedged via the forward market?
e) Given the choice, would you prefer a forward hedge or a money market hedge? Why, and
what is the dollar advantage of one choice over the other?
=> a) Since K (strike price=exercise price) = S1, you should be indifferent. (Since Tay
has a put option for A/R, you will exercise the option if K>S1 and do not
exercise otherwise)
b) In the case of MMH, Tay needs to borrow PV of 250,000 euro from
Germany=250,000*(1/1.02)=245,098.04 euro. Converting this amount to $s results in
245,098.04*1.004=$246,078.43 PV, Certain. FV
of MMH=246,078.43*(1.015)=$249,769.61 FV, Certain.
c) Implied forward rate should be F satisfying 1.015=(1/1.004)*(1.02)*F => F=0.9991
d) 250,000*0.9991=$249,769.61
e) If CIRP holds, FH and MMH are equivalent.
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3. Samsung Inc. has an A/R of $30m due in 90 days. The current spot rate is 1050 Won/$, threemonth forward rate is 1100 Won/$, Korean interest rate is 6%, and US interest rate is 4%. An
option (call or put?) with an exercise rate of 1070 won/$ is available for 5 won/$. Which
alternative (Forward, Money Market, Options) do you recommend, why?
=> You are working for Samsung and want to maximize won receipt of $30m. ($ is a
foreign currency and won is a home currency). FH: 33,000m won FV, Certain,
MMH Borrow PV of $30m=30,000,000*(1/1.01), Convert to
won=30,000,000*(1/1.01)*1050, FV of
MMH=30,000,000*(1/1.01)*1050*(1.015)=31,655,940,594 won FV, Certain. Since FH
is greater than the FV of MMH, FH is preferred. Put Options: The minimum guaranteed
receipt (with a possibility of receiving more from the sale of $30m) is (including the
premium amount subtracted) = (1070-5)*30m = 31.95b won. Put option is a better choice
than MMH since it has a larger amount and has a chance to be even greater. Between FH
and Option, you may think about the difference. If the difference is quite large, then you
may want to consider taking FH although Put options allow you to make a whole lot
more money. Note that Options give you flexibility.
4. Sony Inc. ordered merchandise worth $10M from Xerox Co. and the payment will be due in
three months. Which alternative (FH, MMH, Options) do you recommend using the information
given below, and why? (Compare the ¥ costs of each alternative).
Spot rate
104 ¥/$
Three-month forward rate
101 ¥/$
Japanese three-month interest rate 0.0% per annum
US three-month interest rate
6.0% per annum
Expected future spot rate = 103 ¥/$
A three-month option (call or put?) written on one US dollar is available at an exercise
price of 105 ¥/$ with a premium of 2 yen per dollar.
=> A/P of $10m in 3 months. Objective: minimize yen cost of securing $10m. FH: 1.01B
yen FV, Certain, MMH: Deposit PV of $10m today into an
account=$10,000,000*(1/1.015) To secure this many dollars, the yen payment should be
10,000,000*(1/1.015)*104, FV of this is
10,000,000*(1/1.015)*104*(1.00)=1,024,630,542 yen FV, Certain. Since both FH and
FV of MMH are FV and Certain, you know for sure that FH is a better choice since you
spend less yen to secure $10m. Call Options: the maximum yen cost to secure
$10m including the premium is 1.07 B yen and you may spend less than that. If you think
that the difference between 1.01 B yen and 1.07 B yen, then you may go with FH. If the
difference is rather small, you may go with call options, since you may spend less
than 1.01B yen (including option premium) when S1 becomes very low (99 yen or less).
Given the expected future spot rate is 103 yen/$, it seems that FH may be a better choice
as the prospect of S1 becoming very low (99 yen or less) does not look good.
Chapter 14. Swaps
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1. Explain how the interest rate swap works when Co.A finances its variable rate project yielding
LIBOR+1% with a 10% fixed rate loan, and Co.B funds its fixed rate project yielding 12%, with
a LIBOR% rate loan. Use a diagram to determine a mutual agreeable swap rate. At the swap
rate L for 11%, compute the Locked-in spreads for both companies. What if Big Bank engages
in the swap deal and offers LIBOR% for 10% (or 10% for L depending on your perspective) to
Co.A and LIBOR% for 11% (or 11% for L) to Co.B? Compute the Locked-in spreads for all 3
parties involved in the swap deal.
=> Prior to the swap deal, the spread for Co. A = (L+!)-10=L-9%, while the spread for Co. B =
12 – L. The swap deal of L for 11% should be structured so that Co. A should pay L to Co. B and
get the fixed swap rate 11%. The locked-in-spread for Co. A should be then L-9+(-L+11)=2%.
The locked-in-swap for Co. B should be 12-L+(L-11)=1%. If Big Bank gets involved in the swap
deal, then Co. A’s locked-in-spread becomes L-9+(-L+10)=1% and Co. B will have the same
locked-in-spread. Big Bank’s spread will be 1% as well. You need to draw the diagram.
2. Co. A has an alternative financing cost of LIBOR or 10%, and Co.B has a financing cost of
L+1% or 14%. Using the comparative advantage approach, determine a cost saving strategy.
Determine an arrangement between them so that both can enjoy equal savings. What if there is
a swap bank involved and would like to have all three parties can have the same amount of
savings/profits?
=> Relative to the LIBOR, Co. A has 10% and Co. B has 13% (you take a difference between
the two rates, L+1 – 14=L-13% for Co. B). This suggests that Co. A has a comparative
advantage in the fixed rate at 10% and Co. B has a comparative advantage in the variable rate
(once you choose a comparative advantage for one party, the other party would automatically
have a comparative advantage in an alternative). If both companies choose the rate, where each
has a comparative advantage at, the cost of funding for Co. A becomes 10% (or -10% since it
should be cash outflows) and Co. B has the cost of funding L+1% (or –(L+1)%). Now, if we
introduce a swap deal, L for 11.5% (the mid-point between 10% and 13%), then Co. A should
pay L% to Co. B for 11.5%. The cash flows after the swap deal for each company becomes -10 –
L + 11.5 = -L+1.5 = - (L-1.5%) for Co. A and –(L+1) + L -11.5 = -12.5% for Co. B. Note that
the variable cost of funding for Co. A becomes L-1.5% instead of L% (1.5% reduction) and the
fixed cost of funding for Co. B becomes 12.5% instead of 14% (1.5% savings).
3. Explain how the currency swap works and how it is different from currency forwarding
contracts.
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=> Review the example we used in class. Basically, the currency swap is a series of forward
contracts as both parties exchange payments denominated in different currencies so that both
parties can avoid (or reduce) the foreign currency exposures.
4. Explain debt-equity swap and how all three parties benefit from the swap
=> See your lecture notes.
You may want to read the textbook Chap 14 and the debt for equity swap (pp. 276-278) to have a
good understanding of the subjects.
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