T7-1
INTERNATIONAL ARBITRAGE
Arbitrage - The purchase of a commodity, including foreign
exchange, in one market at one price while simultaneously
selling that same currency in another market at a more
advantageous price, in order to obtain a risk-free profit on
the price differential.
The Arbitrageur is the person who performs the arbitrage.
T7-2
TYPES OF ARBITRAGE
• Locational Arbitrage
• Triangular Arbitrage
• Covered Interest
Arbitrage
T7-3
LOCATIONAL ARBITRAGE
Locational arbitrage involves taking advantage of differential
pricing between locations.
A
B
B .65
A .67
Buy at .67, sell at .68
Buy at .67, sell at .68
Buy at .67, sell at .68...
B .68
A .69
T7-4
TRIANGULAR ARBITRAGE
Triangular Arbitrage (aka “three-point” arbitrage) - involves
taking advantage of unequal cross rates between two
currencies, which is derived from their exchange rates with a
third currency.
T7-5
TRIANGULAR ARBITRAGE
EXAMPLE
London:
New York:
£/DM should be:
Frankfurt:
$/£ = $2.00
$/DM = $.40
.40/2.00 = .2
£/DM = .2
Assume that in London, $/£ is actually = $1.90 (out of line)
• Start with $ and buy £1mil for $1.9mil in London
• Buy DM at £/DM = .2 in Frankfurt (£1mil =
DM5mil)
• Use the DM5mil to buy $ in New York at $/DM =
$.40 (DM5mil * .40 = $2mil)
• Your profit would be $2mil - $1.9mil = $100,000
T7-6
COVERED INTEREST ARBITRAGE
Covered Interest Arbitrage - involves buying or selling
assets internationally (i.e., in more than one country), and
using the forward market to eliminate exchange rate risk, in
order to take advantage of return differentials between the
two countries
• Covered Interest Arbitrage will take place when...
• the interest rate differential between two countries...
• differs from the corresponding forward premium or
discount on the exchange rate between their currencies
T7-7
COVERED INTEREST ARBITRAGE
EXAMPLE
spot £ = $1.00
1-year forward = $1.10 (i.e., forward premium is 10%)
U.S. interest rate = 25%
British interest rate = 10%
note: the difference in interest rates is 15%, which is > the
forward premium
• Borrow £1mil at 10% (£1.1mil due in 1 year)
• Immediately convert the £ to $ and invest the $ at 25%
(grows to $1.25mil)
• Simultaneously enter into a forward contract that
guarantees conversion of £ to $ at £/$ = $1.10
• At year end, deliver $1.25mil, and receive £1,136,364
($1.25mil/$1.10)
• Pay off the £1.1mil and keep the difference (£36,364 *
$1.10 = $40,000 Profit)
T7-8
INTEREST RATE PARITY (IRP)
Interest Rate Parity - the theory states: The difference in the
national interest rates for securities of similar risk and
maturity should be equal to, but opposite in sign to, the
forward rate discount or premium for the foreign currency,
except for transaction costs.
T7-9
IRP EQUATIONS (1)
An = Ending amount of the home currency
Ah = Beginning amount of the home currency
Sj = The spot rate when the foreign currency was purchased
ij = The foreign interest rate
Fj = The forward rate on the foreign currency
(1)
An = (Ah/Sj)*(1+ij)Fj
In words:
End Amt Hm Cur = (Beg Amt Hm Cur/Beg Spot Rate) *
(1+Foreign int rate)*(Forward Rate)
T7-10
IRP EQUATIONS (2)
• Since Fj = Sj(1+p), we can restate eq(1) as:
An = (Ah/Sj)*(1+ij)*[Sj(1+p)]
• Simplifying the above we have eq(2):
(2)
An = Ah(1+ij)*(1+p)
• In words:
End Amt of home currency = (Beg Amt home
currency)*(1 + Foreign int rate) * (1 + forward
premium or discount)
T7-11
IRP EQUATIONS (3)
 The rate of return on an investment is: what you end
up with, minus what you started with, divided by what
you started with.
rj = (An - Ah)/Ah
 Substituting for An in terms of Ah and then simplifying,
we have eq(3), which is the return from covered interest
arbitrage.
(3)
rj = (1+ij)*(1+p) - 1
In words:
 return = (1 + foreign int rate)*(1 + forward premium or
discount) minus 1
T7-12
IRP EQUATIONS (4)
• If Interest Rate Parity exists then...
• The return from covered interest arbitrage...
• should be equal to the rate of return available from
investing domestically
• In equation form we would say:
•
rj = i h
• In words:
•
The return from covered interest arbitrage is equal
to the return on a purely domestic investment of equal
risk
T7-13
•
IRP EQUATIONS (5)
rj = i h
• but from eq(3) we know that

rj = (1+ij)*(1+p) - 1
• therefore



(1+ij)*(1+p) - 1
(1+ij)*(1+p)
(1+p)
= ih
= (1+ih)
= (1+ih)/(1+ij)
T7-14
IRP EQUATIONS (6)
(4)
p = [(1+ih)/(1+ij)] - 1
(Covered Interest Parity)
In words:
The Forward premium or discount on the foreign
currency is equal to (1 + domestic rate) divided by (1
+ foreign rate) minus 1.
T7-15
IRP NUMERICAL EXAMPLE (1)
Spot Rate = 1.00
British Int. Rate = 7.5%
U.S. Int. Rate = 5.2%
• Because the British rates are higher than the U.S.
rates...
• The pound should be selling at a forward discount...
• In order to equalize the returns between the U.S. and
Great Britain
• According to eq(4), that discount should be...
[(1+.052)/(1+.075)] - 1 = -2.14%
T7-16
IRP NUMERICAL EXAMPLE (2)
• if the pound declines in value by 2.14%
• then this will offset the additional British returns
• and the returns to U.S. investors will be the same
whether they invest in the U.S. or Great Britain
• Assuming that the spot rate is 1.00...
•
Fj = Sj(1+p) = 1.00(1-.0214) = .9786
•
1.075 * .9786 = 1.052
T7-17
INTEREST RATE PARITY
• in other words, even if you had invested at the higher
British rate
• by the time you converted your pounds back into
dollars
• your return would have been exactly the same as if you
had simply invested in the U.S. in the first place
T7-18
INTEREST RATE PARITY
A simplified form of the IRP equation:
(5)
p = (Fj - Sj)/Sj  ih - ij
In words:
The forward Premium or Discount (on the Foreign
currency) is approximately equal to the difference
between domestic and foreign interest rates.
T7-19
INTEREST RATE PARITY
Verifying...
-.0214 = (.9786 - 1.00)/1.00 .052 - .075
.052 - .075 = - .0230  -.0214
T7-20
INTEREST RATE PARITY
Foreign Rate > Domestic Rate  Forward Currency
Discount
Foreign Rate < Domestic Rate  Forward Currency
Premium
T7-21
INTEREST RATE PARITY
ih - if (%)
IRP Line
Covered Arbitrage
possible for foreign
investors
Forward
Discount %
Covered Arbitrage
possible for domestic
investors
45 °
Forward
Premium %
T7-22
TESTING IRP
• Regress forward premium (or discount) on the interest
rate differential
•
p = a0 + a1(ih - if) + e
• Check to see if the slope coefficient, a1, is equal to 1.0
(which should be true if on 45 ° line.
• or if the error term, e, is insignificant (which should
also be true if IRP holds.
T7-23
OTHER FACTORS IMPACTING IRP
• Taxes
• Transactions Costs
• Additional Risks
• Currency Restrictions
• Etc.