1. International Arbitrage
Chapter 6
International Arbitrage

2. Chapter Objectives Arbitrage Types of Arbitrage
Realignments due to different types of arbitrage
Interest Rate Parity

3. Arbitrage
Def:
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.

4. Types of Arbitrage Locational arbitrage Triangular arbitrage
Covered interest arbitrage

5. 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.

6. Example 1 Profit = Rs 1 / $ Bank A $ 1 = Rs 85 $ 1 = Rs 86
Buy USD from Bank A
Bank B
$ 1 = Rs 86
Sell it to Bank B
Profit = Rs 1 / $
Bank A
Bank B

7. Example 2 USD/PKR 86.75 /95 * If you trade $100,000
Bank A
USD/PKR /86.25
Bank B
USD/PKR /95
* If you trade $100,000
* Is locational arbitrage possible ?
* Calculate the profit

8. Example 1 Calculations Profit : Rs 0.50 / $ Bank A USD / PKR 86.75 /95
Buy
from Bank
Ask Price of 86.25
Bank B________
USD / PKR /95
Sell
to Bank
bid Price of 86.75
Profit : Rs 0.50 / $
0.50 * 100,000 = Rs 50,000
Bank A
Bank B

9. Problem Beal Bank Yardley Bank Bid price of NZ $ $ 0.401 $ 0.398
Ask price of NZ $ $ $ 0.400
Is locational arbitrage possible?
Assume you have USD 1 M
Calculate the profit

10. Triangular Arbitrage

11. 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

12. Cross Exchange Rate Currency A into currency B
It is an exchange 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

13. 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
Formula
Value of peso in C$= value of peso in USD
value of C$ in USD
= $0.07
$0.70
Therefore 1 Peso = C$ 0.10

14. Triangular Arbitrage USD GBP PKR Value of Rs in $ Value of £ in $

15. Suppose Example 4 GBP/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

16. Calculation Step 1 Convert USD into GBP @ $ 2 $ 10000 / 2 = £ 5000
Step 2 Convert GBP into Rs 112 (Cross Exchange Rate)
£ 5000 * 110 = Rs
Step 3 Covert PKR into $ 0.02
Rs * 0.02 = $ 11000
You Ended with : $ 11000
You Started with: $ 10000
Profit : $

17. Actual Calculation Step 1 Convert USD into GBP $ 2
$ / 2 = £ 5000
Step 2 Convert GBP into Rs 100 (Cross Exchange Rate)
£ 5000 * 100 = Rs
Step 3 Covert PKR into USD $ 0.02
Rs / 50 = $ 10000
You Ended with : $ 10000
You Started with: $ 10000
Profit : $ 0

18. 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 GBP = 100 PKR

19. Realignment due to triangle arbitrage
When the exchange rates of the currencies are not in equilibrium, triangular arbitrage will force them back into equilibrium.

20. Covered interest arbitrage
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.

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

22. Suppose Example 4 GBP/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

23. Investment in UK Investment in US Convert USD into GBP @ $ 2.00 Spot
Deposit in UK 4% Rate
After 3-months Convert principle plus forward rate of $ 2.00
Investment in US
Deposit in US 2% Rate

24. UK Calculation Convert USD into GBP @ $ 2.00 Spot
$ / 2 = £
Deposit in UK 4% Rate
£ * 4 % = £ 20000
After 3-months Convert principle plus $ 2.00 forward rate
(£ £ = £ )
£ * 2.00 = $

25. US Calculation Deposit in US bank @ 2% Rate $ 1000000 * 2 % = $ 20000
$ $20000
Total = $

26. 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 $ more

27. Benefits of understanding the concept of International Arbitrage
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.

28. 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).

29. 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.

30. 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) – 1
premium (1 + foreign interest rate)

31. Determining the Forward Premium
Example:
Suppose 6-month ipeso = 6%, i$ = 5%.
From the U.S. investor’s perspective,
forward premium = 1.05/1.06 – 1 
If S = $.10/peso, then
6-month forward rate = S  (1 + p)
 .10  (1 _ .0094)
 $.09906/peso

32. 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.

33. Graphic Analysis of Interest Rate Parity
Interest Rate Differential (%)
home interest rate – foreign interest rate
Forward
Premium (%)
Discount (%)
- 2
- 4 2 4 1 3
- 1
- 3
IRP line

34. Graphic Analysis of Interest Rate Parity
Interest Rate Differential (%)
home interest rate – foreign interest rate
Forward
Premium (%)
Discount (%)
- 2
- 4 2 4 1 3
- 1
- 3
IRP line
Zone of potential covered interest arbitrage by foreign investors
Zone of potential covered interest arbitrage by local investors

35. 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.

36. 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.

37. 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.

38. Considerations When Assessing IRP
Transaction 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

39. Considerations When Assessing IRP
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.

40. Explaining Changes in Forward Premiums
Because of IRP,
a forward rate
will normally move in tandem with the spot rate.
This correlation depends on interest rate movements,
i.e. p  iH–iF t0 t2 t1
Interest Rates iA
iU.S.
time
Forward Rates
Spot and SA FA

41. Explaining Changes in Forward Premiums
During the 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.

42. Impact of Arbitrage on an MNC’s Value
E (CFj,t ) = expected cash flows in currency j to be received by the U.S. parent at the end of period t
E (ERj,t ) = expected exchange rate at which currency j can be converted to dollars at the end of period t
k = weighted average cost of capital of the parent
Forces of Arbitrage

43. Chapter Review International Arbitrage Locational Arbitrage
Triangular Arbitrage
Covered Interest Arbitrage
Comparison of Arbitrage Effects

44. 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

45. Chapter Review Explaining Changes in Forward Premiums
Impact of Arbitrage on an MNC’s Value