Chapter 6
International Arbitrage and
Interest rate Parity
Rashedul Hasan
International Arbitrage
Arbitrage can be loosely defined as capitalizing on a
discrepancy in quoted prices by making a riskless
profit. Now a days, exchange rates are quoted not only
against dollars, but also quoted against other important
currencies like Euro, pound, DM, Lira, Yen, Rupee etc.
This facilitates arbitrageur to buy foreign currency at a
lower rate from one market and sell at higher rate in
another market, as there is exchange rate inconsistency
exists in different money center. Often, the funds
invested are not tied up and no risk is involved.
For example, tow coin shops buy and sell
coins. If shop A is willing to sell a particular
coin for $ 120, while Shop B is willing to
buy that same coin for $ 130, a person can
execute arbitrage by purchasing the coin at
shop A for $ 120 and selling it to shop B for
$ 130. if two coin shops are not aware of
each other’s price, the opportunity of
arbitraging may occur.
Types of Arbitrage
Locational arbitrage
Triangular arbitrage
Covered interest arbitrage
Locational arbitrage
Locational arbitrage is possible when a bank’s buying
price (bid price) is higher than another bank’s selling
price (ask price) for the same currency.
Locational arbitrage is normally conducted by banks or
other foreign exchange dealers whose computers can
continuously monitor the quotes provided by other
banks. If the 3rd Bank noticed a discrepnncy between
1st Bank and 2nd Bank, they would quickly engage in
locational arbitrage to earn immediate risk-free profit.
International Arbitrage
• Locational arbitrage is possible when a bank’s
•
buying price (bid price) is higher than another
bank’s selling price (ask price) for the same
currency.
Example:
Bank C Bid
NZ$
$.635
Ask
$.640
Bank D Bid
NZ$
$.645
Ask
$.650
Buy NZ$ from Bank C @ $.640, and sell it to Bank D @
$.645. Profit = $.005/NZ$.
Gains from Locational
Arbitrage
• Buy NZ$ from Bank C @ $.640, and sell it
to Bank D @ $.645. Profit = $.005/NZ$.
• A person can obtain New Zealand dollars
for “Bank A” at the ask price of $.640 and
then sell New Zealand dollars to “Bank B”
at the bid price of $.645. This represent a
“one round trip” transaction in Locational
arbitrage.
•
• If you start with $ 10,000 and conduct one round
trip transaction, how many US$ will you endup with
?
• The $ 10,000 is initially exchanged for NZ$
($10,000/$.640 per NZ$) = NZ$ 15,625 at Bank A”
• Then NZ$ 15,625 are sold for $ .645 each =
(15,625*.645) = $ 10,078.
• Thus Profit/Gain = ( $10,078-$10,000) = $78.
International Arbitrage
• Triangular arbitrage is possible when a cross
exchange rate quote differs from the rate calculated
from spot rates. Cross exchange rate refers to the
relationship between two nondollar currency.
• Example:
Bid
Ask
British pound (£)
$1.60
$1.61
Malaysian ringgit (MYR)
$.200
$.202
£
MYR8.1
MYR8.2
Buy £ @ $1.61, convert @ MYR8.1/£, then sell MYR @
$.200. Profit = $.01/£. (8.1.2=1.62)
Triangular arbitrage
• Assume that, a bank has qouted the British pound (£) at
$ 1.60, the Malaysian Ringgit (MYR) at $ .20, and the
cross exchange rate at £ 1 = MYR 8.1.
• Your first tast would be determine the cross exchange
rate that is Pound should be worth MYR8.0
• When qouting an exchange rate of £ 1 = .81, the bank is
exchanging too many Ringgit for a pound and is asking
for too many Ringgit in exchange for a pound. Based on
this information, you can engage in triangular arbitrage
by purchasing pounds with dollar, converting the Pounds
to Ringgit and then exchanging the Ringgit for dollars.
• If you have $ 10,000, how many dollars will you end up
with it you implement this triangular arbitrage strategy
• [1] determine the number of pounds received for your
dollars: $ 10,000 = £ 6,250 ( $ 10,000 / 1.60) based on the
banks qoute of $ 1.60 per pound.
• [2] determine how many ringgit you will receive in
exchange for for pounds : £ 6,250 = MYR 50,625
• (£ 6,250*8.1) based on the banks qoute of 8.1 ringgit per
pound.
• [3] Determine how many US$ you will receive in exchange
for the ringgit: MYR50,625 = $ 10,125
• (MYR50,625*.20) based on the bank’s qoute of $.20 per
ringgit ( 5 ringgit to the dollar)
• [4] the triangular arbitrage strategy will generates $ 10,125.
which is $ 125 more ($ 10,125 - $ 10,000) more than you
starred with.
• Buy £ @ $1.61, convert @ MYR8.1/£, then
sell MYR @ $.200. Profit = $.01/£.
(8.1*.2=1.62)
• When the exchange rates of the currencies
are not in equilibrium, triangular arbitrage
will force them back into equilibrium.
Impact of Triangular Arbitrage
Activity
Impact
1. Participants use dollars to purchase
pounds.
Bank increases its ask price for Pounds
with respect to dollar
2. Participants use pounds to purchase
Malaysian Ringgit
Bank reduces its bid price of the Pound
with respect to the ringgit, that is, it
reduces the number of ringgit to be
exechanged per pound received.
3. Participants use Malaysian Ringgit to
purchase U.S. $
Bank reduces its bid price of ringgit
with respect to the dollar.
International Arbitrage
$
Value of
£ in $
£
Value of
MYR in $
Value of
£ in MYR
MYR
• When the exchange rates of the currencies are
not in equilibrium, triangular arbitrage will
force them back into equilibrium.
Covered interest arbitrage
• Covered interest arbitrage is the process of capitalizing
on the interest rate differential between two countries,
while covering for exchange rate risk.
• The logic of the term Covered interest arbitrage become
clear when it is broken into two parts; “interest arbitrage”
and “covered”.
• Interest arbitrage refers to the process of capitalizing on
the difference between interest rates between two
countries. On the other hand, Covered refers to hedging
your position against exchange rate risk.
• Example,
• You desire to capitalize on relatively high rates of
interest rate in the U.K. and have fund available
for 90 days. The interest rate is certain but only the
future exchange rate at which you will exchange
pounds back to U.S. dollars is uncertain. You can
use a forward sale of pounds to gurantee the rate at
which you can exchange pounds for dollars at a
future point of time. The actual strategy is as
follows,
• [1] On day 1, convert your U.S. dollars to pound
and set up a 90-day deposit account in a British
bank.
• [2] On day 1, engage in a forward contractto sell
pounds 90 days forward.
• [3] In 90 days when the deposit matures, convert
the pounds to U.S. dollars at the rate that was
agreed upon in the forward contract.
Assume the following information
• You have $80,000 to invest
• £ spot rate = $1.60
• 90-day forward rate of the £ = $1.60
• U.S. 90-day interest rate = 2%
• U.K. 90-day interest rate = 4%
• Based on the information you may proceed,
• [1] On day 1, convert $80,000 to £50,000
($80,000/1.60) and deposit the amount in a British bank.
• [2] On day 1, Sell £ 52,000, 90-days forward. By the
time the deposit matures, you will have £ 52,000
including interest.
• [3] In 90 days when the deposit matures, you can fulfill
your forward contract obligation by converting your £
52,000 into $ 83,200 (£ 52,000*$1.60) based on forward
contract rate of $ 1.60 per pound.
Impact of Triangular Arbitrage
Activity
Impact
1. Use dollars to purchase pounds in Upward pressure on the spot rate of
the spot market.
the pound.
2. Engage in forward contract to sell Downward pressure on the forward
pounds forward
rate of the pound
3. invest funds from the U.S. in the
U.K.
Possible Upward pressure on U.S.
interest rates and Downward
pressure on the British Interest rate.
• Locational arbitrage ensures that quoted exchange rates
are similar across banks in different locations.
• Triangular arbitrage ensures that cross exchange rates
are set properly.
• Covered interest arbitrage ensures that forward
exchange rates are set properly.
• Any discrepancy will trigger arbitrage, which will then
eliminate the discrepancy. Arbitrage thus makes the
foreign exchange market more orderly.
Interest Rate Parity (IRP)
• Once market forces cause interest rates and exchange
rates to adjust such that covered interest arbitrage is no
longer feasible, there is an equilibrium state referred to
as Interest rate Parity.
• Market forces cause the forward rate to differ from the
spot rate by an amount that is sufficient to offset the
interest rate differential between the two currencies.
• Then, covered interest arbitrage is no longer feasible,
and the equilibrium state achieved is referred to as
interest rate parity (IRP).