Tutorial 5: Answers
Questions
1. Locational Arbitrage. Explain the concept of locational arbitrage and the scenario
necessary for it to be plausible.
ANSWER: Locational arbitrage can occur when the spot rate of a given currency
varies among locations. Specifically, the ask rate at one location must be lower than
the bid rate at another location. The disparity in rates can occur since information is
not always immediately available to all banks. If a disparity does exist, locational
arbitrage is possible; as it occurs, the spot rates among locations should become
realigned.
2. Triangular Arbitrage. Explain the concept of triangular arbitrage and the scenario
necessary for it to be plausible.
ANSWER: Triangular arbitrage is possible when the actual cross exchange rate
between two currencies differs from what it should be. The appropriate cross rate can
be determined given the values of the two currencies with respect to some other
currency.
3. Covered Interest Arbitrage. Explain the concept of covered interest arbitrage and
the scenario necessary for it to be plausible.
ANSWER: Covered interest arbitrage involves the short-term investment in a foreign
currency that is covered by a forward contract to sell that currency when the
investment matures. Covered interest arbitrage is plausible when the forward
premium does not reflect the interest rate differential between two countries specified
by the interest rate parity formula. If transactions costs or other considerations are
involved, the excess profit from covered interest arbitrage must more than offset these
other considerations for covered interest arbitrage to be plausible.
4. Interest Rate Parity. Explain the concept of interest rate parity. Provide the rationale
for its possible existence.
ANSWER: Interest rate parity states that the forward rate premium (or discount) of a
currency should reflect the differential in interest rates between the two countries. If
interest rate parity didn't exist, covered interest arbitrage could occur (in the absence
of transactions costs, and foreign risk), which should cause market forces to move
back toward conditions which reflect interest rate parity. For further explanation and
the exact formula, please refer to lecture notes or the chapter in the text.
5. Inflation Effects on the Forward Rate. Why do you think currencies of countries
with high inflation rates tend to have forward discounts?
ANSWER: These currencies have high interest rates, which cause forward rates to
have discounts as a result of interest rate parity.
6. Changes in Forward Premiums. Assume that the Japanese yen’s forward rate
currently exhibits a premium of 6 percent and that interest rate parity exists. If U.S.
interest rates decrease, how must this premium change to maintain interest rate
parity? Why might we expect the premium to change?
ANSWER: The premium will decrease in order to maintain IRP, because the
difference between the interest rates is reduced. We would expect the premium to
change because as U.S. interest rates decrease, U.S. investors could benefit from
covered interest arbitrage if the forward premium stays the same. The return earned
by U.S. investors who use covered interest arbitrage would not be any higher than
before, but the return would now exceed the interest rate earned in the U.S. Thus,
there is downward pressure on the forward premium.
7. Testing Interest Rate Parity. Describe a method for testing whether interest rate
parity exists. Why are transactions costs, currency restrictions, and differential tax laws
important when evaluating whether covered interest arbitrage can be beneficial?
ANSWER: At any point in time, identify the interest rates of the U.S. versus some
foreign country. Then determine the forward rate premium (or discount) that should
exist according to interest rate parity. Then determine whether this computed forward
rate premium (or discount) is different from the actual premium (or discount).
Even if interest rate parity does not hold, covered interest arbitrage could be of no
benefit if transactions costs or tax laws offset any excess gain. In addition, currency
restrictions enforced by a foreign government may disrupt the act of covered interest
arbitrage.
Problems
1. Locational Arbitrage. Assume the following information:
Bid price of New Zealand dollar
Ask price of New Zealand dollar
Beal Bank Yardley Bank
$.401
$.398
$.404
$.400
Given this information, is locational arbitrage possible? If so, explain the steps
involved in locational arbitrage, and compute the profit from this arbitrage if you had
$1,000,000 to use. What market forces would occur to eliminate any further
possibilities of locational arbitrage?
ANSWER: Yes! One could purchase New Zealand dollars at Yardley Bank for $.40
and sell them to Beal Bank for $.401. With $1 million available, 2.5 million New
Zealand dollars could be purchased at Yardley Bank. These New Zealand dollars
could then be sold to Beal Bank for $1,002,500, thereby generating a profit of $2,500.
The large demand for New Zealand dollars at Yardley Bank will force this bank's ask
price on New Zealand dollars to increase. The large sales of New Zealand dollars to
Beal Bank will force its bid price down. Once the ask price of Yardley Bank is no
longer less than the bid price of Beal Bank, locational arbitrage will no longer be
beneficial.
2. Triangular Arbitrage. Assume the following information:
Value of Canadian dollar in U.S. dollars
Value of New Zealand dollar in U.S. dollars
Value of Canadian dollar in New Zealand dollars
Quoted Price
$.90
$.30
NZ$3.02
Given this information, is triangular arbitrage possible? If so, explain the steps
that would reflect triangular arbitrage, and compute the profit from this strategy if you
had $1,000,000 to use. What market forces would occur to eliminate any further
possibilities of triangular arbitrage?
ANSWER: Yes. The appropriate cross exchange rate should be 1 Canadian dollar =
3 New Zealand dollars. [US$/CAD x 1/(US$/NZD) = NZD/CAD] Thus, the
actual value of the Canadian dollars in terms of New Zealand dollars is more than
what it should be. One could obtain Canadian dollars with U.S. dollars, sell the
Canadian dollars for New Zealand dollars and then exchange New Zealand dollars for
U.S. dollars. With $1,000,000, this strategy would generate $1,006,667 thereby
representing a profit of $6,667.
[$1,000,000/$.90 = C$1,111,111 × 3.02 = NZ$3,355,556 × $.30 = $1,006,667]
Start = US$1.000000 million
End = US$1.006667 million
Buy CAD @ US$0.90
Sell NZD @ US$0.30
Implied cross rate:
Buy CAD @
NZD 3.00
NZ$3,355,556
Market cross rate: Sell
CAD @ NZD3.02
C$1,111,111
The diagram shows that you are
essentially buying CAD at the
implied cross rate of NZD 3.00
and then selling it at the market
cross rate of NZD 3.02.
The value of the Canadian dollar with respect to the U.S. dollar would rise. The value of
the Canadian dollar with respect to the New Zealand dollar would decline. The value of
the New Zealand dollar with respect to the U.S. dollar would fall.
[Note: You should be prepared to analyse and identify what would happen to the
currency exchange rates as a result of this arbitrage. Basically, for each step of the
transaction, imagine how the prices can get worse for the arbitrageur. For example, in
the first step (USDCAD), the worst thing for the arbitrageur is if the CAD she is
buying gets more expensive, relative to USD. This is likely what will happen to the prices
as a result of arbitrage – prices get worse and worse from supply/demand until arbitrage
is no longer profitable. At this point of no further arbitrage, the market reaches
equilibrium.]
3. Covered Interest Arbitrage. Assume that the one-year U.S. interest rate is 11
percent, while the one-year interest rate in Malaysia is 40 percent. Assume that a
U.S. bank is willing to purchase the currency of that country from you one year from
now at a discount of 13 percent. Would covered interest arbitrage be worth
considering? Explain. Calculate the yield from covered interest arbitrage for a US
investor. Is there any reason why a US investor should not attempt covered interest
arbitrage in this situation? (Ignore tax effects.)
Please note that this question has been slightly modified.
ANSWER:
Since the interest rate differential 29% (40%-11%) is much higher than the one year
forward rate discount 13%, covered interest arbitrage appears to be worth
considering.
By given, F ($/MY)= (1-0.13) x S($/MY) = 0.87 S($/MY)
[Note: ‘F’ stands for forward, while ‘S’ stands for spot. The base currency is MYR. When
we say the base currency is at a forward discount, that means the number of US$
being paid per 1 MYR on the forward (F) is 13% less than the spot (S) rate. ]
Assuming a $1,000,000 initial investment by a US investor, the covered interest arbitrage
would generate:
$1,000,000 × 1/S($/MY) × (1.40) × [0.87 S($/MY)] = $1,218,000
Yield = ($1,218,000 – $1,000,000)/$1,000,000 = 21.8%
Thus, covered interest arbitrage would be worth considering since the return would be
21.8 percent, which is much higher than the U.S. interest rate.
However, if the funds would be invested in Malaysia, that could cause some concern
about default risk or government restrictions on convertibility of the currency back to
dollars.
[Note: The worked example skips some logical steps. Step-by-step, the reasoning is:


MYR is worth 13% less in one-year’s time (valued in USD) compared to today.
On the other hand, investing in MYR for one year returns 40%-11% = 29% more
than it costs to borrow USD.
Hence you get more from the one-year interest difference (invest MYR, borrow
USD) compared to the loss you face when you need to convert MYR back to USD
in one year’s time.

Therefore, you should do the following transaction:
Deposit
= MYR 1 million / S
Receive =
MYR [1 million / S] x (1.40)
Forward exchange rate USD/MYR
= F = S x (1-0.13)
Spot exchange rate
USD/MYR = S
Borrow USD 1
million
Receive = USD [1 million / S] x (1.40) x S (1-0.13)
Pay = USD 1 million x (1.11)
P&L = Receive –Pay = US 1 million x (1.218-1.11)
Also note the following assumptions:
 No bid/ask spreads.
 No transaction costs.
 Very, very importantly – it just so happens that the holding period in this example
is exactly one year so that you can directly compare the interest rate difference
(% p.a.) versus the spot/forward difference (% absolute). In the more common
case when the holding period is not one year, then you need to annualize the
spot/forward differential in order to make it comparable to the interest rate
differential. Alternatively, as in the next example, you can pro rata the annual
interest rate to find the absolute interest rate per holding period.
 Once all the legs of this transaction are executed, there is no further market risk
for the arbitrageur – P&L is locked in. Are there other kinds of risk, though?
]
4. Covered Interest Arbitrage in Both Directions. The following information is
available:
 You have $500,000 to invest
 The current spot rate (S) of the Moroccan dirham is $.110.
 The 60-day forward rate (F) of the Moroccan dirham is $.108.
 The 60-day interest rate in the U.S. is 1 percent (i.e 6% pa)
 The 60-day interest rate in Morocco is 2 percent (i.e 12% pa)
a. What is the yield to a U.S. investor who conducts covered interest arbitrage?
Did covered interest arbitrage work for the investor in this case?
b. Would covered interest arbitrage be possible for a Moroccan investor in this
case?
ANSWER:
a. Covered interest arbitrage (for US based investor) would involve the following
steps:
1. Convert dollars to Moroccan dirham: $500,000/$.11 = MD4,545,454.55
2. Deposit the dirham in a Moroccan bank for 60 days. You will have
MD4,545,454.55 × (1.02) = MD4,636,363.64 in 60 days.
3. In 60 days, convert the dirham back to dollars at the forward rate and
receive MD4,636,363.64 × $.108 = $500,727.27
The yield to the U.S. investor is $500,727.27/$500,000 – 1 = .15%. As the yield
is smaller than the US interest rate 1%, the covered interest arbitrage did not
work for the investor in this case. The lower Moroccan forward rate more than
offsets the higher interest rate in Morocco.
OR
$500,000 invested in the US for 60 days will become $505,000 (=$500000 x
1.01) which is higher than the amount generated by covered interest arbitrage.
b. Yes, covered interest arbitrage would be possible for a Moroccan investor. The
investor would convert dirham to dollars, invest the dollars at a 1 percent
interest rate in the U.S., and sell the dollars forward 60 days. Even though the
Moroccan investor would earn an interest rate that is 1 percent lower in the
U.S., the forward rate discount of the dirham more than offsets that differential.
Verify?
5. Testing IRP. The one-year interest rate in Singapore is 11 percent. The one-year
interest rate in the U.S. is 6 percent. The spot rate of the Singapore dollar (S$) is $.50
and the one year forward rate of the S$ is $.46. Assume zero transactions costs.
Note: IRP states that:
(1 + i$) / (1 + i¥) = F($/¥) / S($/¥)
Or approximately:
Interest rate differential (i$ - i¥) ≈ (F-S) / S = forward prem/discount (on¥ against $)
[Note – substitute S$ for ‘¥’. The first equation is the exact IRP equation while the
second is only an approximation.
Also, be very careful – for the exact IRP formula, term currency interest rate is in the
numerator, base currency interest rate is in the denominator.]
a.
Does interest rate parity exist?
ANSWER: No, because if IRP holds, then
1.06 / 1.11 = 0.46/0.50
Or
0.9550 = 0.9200, which is not true.
[Note: you can also use these results to answer part (b) and (c) below. The ‘trick’ is as
follows:
Left Hand Side (LHS) is too high relative to RHS, versus IRP. This means the
numerator of LHS is too big, denominator of LHS is too small. i.e. term interest
rate is too high, base interest rate is too low, relative to IRP. Therefore, you
should borrow the base interest rate, and lend the term interest rate.]
b.
Can a U.S. firm benefit from investing funds in Singapore using covered
interest arbitrage?
ANSWER: No, because the discount on a forward sale [=(0.50-0.46)/0.50] exceeds the
interest rate advantage (=0.11-0.06) of investing in Singapore.
Alternatively, students can show that the rate of return achieved by the US firm from
an investment in Singapore will be lower than interest rate in the US [i.e. use covered
interest arbitrage to demonstrate that not profitable to borrow USD to invest in SGD
and cover with the forward. Question – assuming no bid/ask spreads, does this mean
NO covered interest arbitrage is possible at all?].
[Note: In other words, IRP and covered interest arbitrage (CIA) are directly related:
 If IRP equation is true  No CIA is possible
 If CIA is possible  IRP does not hold
]
6. Deriving the Forward Rate. Assume that annual interest rates in the U.S. are 4
percent, while interest rates in France are 6 percent.
a. According to IRP, what should the forward rate premium or discount of the euro
be?
b. If the euro’s spot rate is $1.10, what should the one-year forward rate of the euro
be?
ANSWER:
Using IRP conditions, we get:
(1.04)
 1  .0189  1.89%
a. p 
(1.06)
This suggests that if IRP holds, then euro will be at a forward discount of 1.89%
against the US dollar.
[note: this form of the exact IRP equation implies that the forward rate is defined
as : F = S (1+p)]
b. F  $1.10(1  .0189)  $1.079
This suggests that if IRP holds, then the one year forward rate of euro would be
US$1.079.
7. Covered Interest Arbitrage in Both Directions. Assume that the annual U.S. interest
rate is currently 8 percent and Germany’s annual interest rate is currently 9 percent.
The euro’s one-year forward rate currently exhibits a discount of 2 percent.
a. Does interest rate parity exist?
ANSWER: No, because the discount on euro (= 2%) is larger than the interest rate
differential (= 1%)
b. Can a U.S. firm benefit from investing funds in Germany using covered interest
arbitrage?
ANSWER: No, because the discount on a forward sale exceeds the interest rate
advantage of investing in Germany.
c. Can a German subsidiary of a U.S. firm benefit by investing funds in the United
States through covered interest arbitrage?
ANSWER: Yes, because even though it would earn 1 percent less interest over the
year by investing in U.S. dollars, it would be able to sell dollars for 2 percent more
than it paid for them (it would be buying euros forward at a discount of 2 percent).
[Note: these numbers are only rough, since they use the approximate form of the IRP
equation. As an exercise, work out the exact P&L by doing covered interest arbitrage!]