Chapter 6

International Arbitrage

Chapter Objectives Arbitrage

Types of Arbitrage

Realignments due to different types of arbitrage

Interest Rate Parity

ArbitrageDef:

Capitalizing on a discrepancy in quoted prices. Often, the funds invested are not tied up for any length of time and no risk is involved.

In response to the imbalance in demand and supply resulting from arbitrage activity, prices will realign very quickly, such that no further risk-free profits can be made.

Locational arbitrageTriangular arbitrageCovered interest arbitrage

Types of Arbitrage

Locational arbitrage

“Action to capitalize on discrepancy in quoted exchange rates between banks”

It becomes possible when a bank’s buying price is higher than another bank’s selling price for the same currency.

Example 1

Bank A$ 1 = Rs 85

Buy USD from Bank A

Bank B $ 1 = Rs 86

Sell it to Bank B

Profit = Rs 1 / $

Bank A Bank B

Example 2

Bank AUSD/PKR 85.15 /86.25

Bank B

USD/PKR 86.75 /95

* If you trade $100,000

* Is locational arbitrage possible ?

* Calculate the profit

Example 1

Calculations Bank AUSD / PKR 85.15 /86.25

Buy from Bank A @Ask Price of 86.25

Bank B________ USD / PKR 86.75 /95

Sell to Bank B @ bid Price of 86.75

Profit : Rs 0.50 / $

0.50 * 100,000 = Rs 50,000

Bank A Bank B

Problem

Beal Bank Yardley Bank

Bid price of NZ $ $ 0.401 $ 0.398

Ask price of NZ $ $ 0.404 $ 0.400

Is locational arbitrage possible? Assume you have USD 1 M Calculate the profit

Triangular Arbitrage

“Action to capitalize on a discrepancy where the quoted cross exchange rate is not equal to the rate that should exist at equilibrium”

It is possible when a cross exchange rate quote differs from the rate calculated from spot rates

Triangular arbitrage

Cross Exchange Rate It is an exchange rate @ which currencies other

than US dollar can be exchanged

Here we are concerned with exchanging

Currency A into currency B by using Rate of Currency A in terms of US- dollar & Rate of Currency B in terms of US- dollar

Example 3 A Canadian firm needs Mexican Peso to buy Mexican

goods It has to find the peso value relative to Canadian $ This type of rate is termed as Cross Exchange rate

FormulaValue of peso in C$= value of peso in USD value of C$ in USD = $0.07 $0.70

Therefore 1 Peso = C$ 0.10

Triangular Arbitrage

USD

GBPPKR

Value of Rs in $

Value of £ in $

Value ofRs in £

SupposeGBP/USD spot rate: $ 2.00

GBP/PKR Cross Exchange rate: Rs 112

PKR/USD Spot rate: $ 0.02

Is triangular arbitrage possible Calculate the profit from triangular arbitrage

Example 4

Calculation

Step 1 Convert USD into GBP @ $ 2 $ 10000 / 2 = £ 5000

Step 2 Convert GBP into PKR @ Rs 112 (Cross Exchange Rate)

£ 5000 * 110 = Rs 550000

Step 3 Covert PKR into USD @ $ 0.02 Rs 550000 * 0.02 = $ 11000

You Ended with : $ 11000You Started with: $ 10000 Profit : $ 1000

Actual Calculation

Step 1 Convert USD into GBP $ 2

$ 10000 / 2 = £ 5000

Step 2 Convert GBP into PKR @ Rs 100 (Cross Exchange Rate)

£ 5000 * 100 = Rs 500000

Step 3 Covert PKR into USD $ 0.02

Rs 500000 / 50 = $ 10000

You Ended with : $ 10000

You Started with: $ 10000

Profit : $ 0

Cross Exchange Rate We have to find the GBP value relative to PKR This type of rate is termed as Cross Exchange rate

Formula

Value of GBP in PKR= value of GBP in USD

value of PKR in USD

= $ 2

$ 0.02

Therefore 1 GBP = 100 PKR

Realignment due to triangle arbitrage

When the exchange rates of the currencies are not in equilibrium, triangular arbitrage will force them back into equilibrium.

Investment in a foreign money market security with a simultaneous forward sale of the currency denominating that security

It is the process of capitalizing on the interest rate differential between two countries and covering the exchange rate risk through forward contract.

Covered interest arbitrage

Covered interest arbitrage tends to force a relationship between forward rate premiums and interest rate differentials.

SupposeGBP/USD spot rate: $ 2.00

Interest rate on U.S. 90-day Deposit = 2%

Interest rate on U.K. 90-day Deposit = 4%

3-month forward : $ 2.00

Example 4

Investment in UK Convert USD into GBP @ $ 2.00 Spot Deposit in UK bank @ 4% Rate After 3-months Convert principle plus

interest @ forward rate of $ 2.00

Investment in US Deposit in US bank @ 2% Rate

UK Calculation Convert USD into GBP @ $ 2.00 Spot

$1000000 / 2 = £ 500000 Deposit in UK bank @ 4% Rate

£ 500000 * 4 % = £ 20000 After 3-months Convert principle plus

interest @ $ 2.00 forward rate

(£ 500000 + £ 20000 = £ 520000)

£ 520000 * 2.00 = $ 1040000

US CalculationDeposit in US bank @ 2% Rate $ 1000000 * 2 % = $ 20000

$ 1000000 + $20000

Total = $1020000

Comparing Profits

From UK $ 1040000 From US $ 1020000

Therefore it is better to take the benefit of interest rate differential and deposit in UK

You can achieve profit of $ 20000 more

Locational arbitrage

It ensures that quoted exchange rates are similar across banks in different locations.

Triangular arbitrage

It ensures that cross exchange rates are set properly.

Covered interest arbitrage

It ensures that forward exchange rates are set properly.

Benefits of understanding the concept of International Arbitrage

Interest Rate Parity (IRP)

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).

Testing IRP When IRP exists, the rate of return achieved from

covered interest arbitrage should equal the rate of return available in the home country.

End-value of a $1 investment in covered interest arbitrage = (1/S) (1+iF) F

= (1/S) (1+iF) [S (1+p)]

= (1+iF) (1+p)

where p is the forward premium.

Derivation of IRP

End-value of a $1 investment in the home country = 1 + iH

Equating the two and rearranging terms:

p = (1+iH) – 1(1+iF)

i.e. forward = (1 + home interest rate) – 1premium (1 + foreign interest rate)

Determining the Forward PremiumExample: Suppose 6-month ipeso = 6%, i$ = 5%. From the U.S. investor’s perspective,

forward premium = 1.05/1.06 – 1 - .0094 If S = $.10/peso, then

6-month forward rate = S (1 + p)

.10 (1 _ .0094)

$.09906/peso

Determining the Forward Premium Note that the IRP relationship can be

rewritten as follows:F – S = S(1+p) – S = p = (1+iH) – 1 = (iH–iF)

S S (1+iF) (1+iF)

The approximated form, p iH–iF, provides a reasonable estimate when the interest rate differential is small.

Graphic Analysis of Interest Rate Parity

Interest Rate Differential (%)home interest rate – foreign interest rate

ForwardPremium (%)

ForwardDiscount (%)

- 2

- 4

2

4

1 3- 1- 3

IRP line

Graphic Analysis of Interest Rate Parity

Interest Rate Differential (%)home interest rate – foreign interest rate

ForwardPremium (%)

ForwardDiscount (%)

- 2

- 4

2

4

1 3- 1- 3

IRP line

Zone of potential covered interest

arbitrage by local investors

Zone of potential covered interest

arbitrage by foreign investors

Test for the Existence of IRP

To test whether IRP exists, collect the actual interest rate differentials and forward premiums for various currencies. Pair up data that occur at the same point in time and that involve the same currencies, and plot the points on a graph.

IRP holds when covered interest arbitrage is not worthwhile.

Interpretation of IRP

When IRP exists, it does not mean that both local and foreign investors will earn the same returns.

What it means is that investors cannot use covered interest arbitrage to achieve higher returns than those achievable in their respective home countries.

Does IRP Hold?

Various empirical studies indicate that IRP generally holds.

While there are deviations from IRP, they are often not large enough to make covered interest arbitrage worthwhile.

This is due to the characteristics of foreign investments, including transaction costs, political risk, and differential tax laws.

Considerations When Assessing IRPTransaction Costs

iH – iF

p

Zone of potential covered interest

arbitrage by foreign investors Zone of

potential covered interest

arbitrage by local

investors

IRP line

Zone where covered interest arbitrage is not feasible due to

transaction costs

Political Risk A crisis in the foreign country could cause its

government to restrict any exchange of the local currency for other currencies.

Investors may also perceive a higher default risk on foreign investments.

Differential Tax Laws If tax laws vary, after-tax returns should be

considered instead of before-tax returns.

Considerations When Assessing IRP

Because of IRP,a forward ratewill normally move in tandem with the spot rate.

This correlation depends on interest rate movements, i.e. p iH–iF

t0 t2t1

Inte

rest

Rat

es iA

iU.S.

time

t0 t2t1

Sp

ot

and

Fo

rwar

d R

ates

SA

FA

time

Explaining Changes in Forward Premiums

Explaining Changes in Forward Premiums

During the 1997-98 Asian crisis, the forward rates offered to U.S. firms on some Asian currencies were substantially reduced for two reasons.

The spot rates of these currencies declined substantially during the crisis.

Their interest rates had increased as their governments attempted to discourage investors from pulling out their funds.

Impact of Arbitrage on an MNC’s Value

n

tt

m

jtjtj

k1=

1 , ,

1

ER ECF E

= Value

E (CFj,t ) = expected cash flows in currency j to be received by the U.S. parent at the end of period tE (ERj,t ) = expected exchange rate at which currency j can be converted to dollars at the end of period tk = weighted average cost of capital of the parent

Forces of Arbitrage

International Arbitrage Locational Arbitrage Triangular Arbitrage Covered Interest Arbitrage Comparison of Arbitrage Effects

Chapter Review

Chapter Review

Interest Rate Parity (IRP) Derivation of IRP Determining the Forward Premium Graphic Analysis of IRP Test for the Existence of IRP Interpretation of IRP Does IRP Hold? Considerations When Assessing IRP

Chapter Review

Explaining Changes in Forward Premiums Impact of Arbitrage on an MNC’s Value