1. Chapter 7 International Arbitrage and Interest Rate Policy
International Financial Management, 2nd edition
Jeff Madura and Roland Fox
ISBN © 2011 Cengage Learning EMEA

2. Chapter Objectives
To explain the conditions that will result in various forms of international arbitrage, along with the realignments that will occur in response.
To explain the concept of interest rate parity, and how it prevents arbitrage opportunities.
International Financial Management, 2nd edition
Jeff Madura and Roland Fox
ISBN © 2011 Cengage Learning EMEA

3. International Arbitrage (1)
Arbitrage can be loosely defined as capitalizing on a discrepancy in quoted prices to make a riskless profit.
The effect of arbitrage on demand and supply is to cause prices to realign, such that no further risk-free profits can be made.
International Financial Management, 2nd edition
Jeff Madura and Roland Fox
ISBN © 2011 Cengage Learning EMEA

4. International Arbitrage (2)
As applied to foreign exchange and international money markets, arbitrage takes three common forms:
locational arbitrage
triangular arbitrage
covered interest arbitrage
International Financial Management, 2nd edition
Jeff Madura and Roland Fox
ISBN © 2011 Cengage Learning EMEA

5. 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.
Example
Bank C Bid Ask Bank D Bid Ask
NZ$ $.635 $.640 NZ$ $.645 $.650
Buy NZ$ from Bank $0.64, and sell it to Bank $0.645 Profit = $.005/NZ$.
International Financial Management, 2nd edition
Jeff Madura and Roland Fox
ISBN © 2011 Cengage Learning EMEA

6. Triangular arbitrage Assume you have the following quotations
Triangular arbitrage is possible when a cross exchange rate quote differs from the rate calculated from spot rate quotes.
Assume you have the following quotations
$ to play with
Westminster Bank: $ /£
Shanghai Bank € /£
Wells Fargo $ /€
Is triangular arbitrage possible ?
Cross rate $/€ = 1.55/1.50 =
Sell $ where it`s expensive, buy it back where it`s cheap

7. Triangular arbitrage

8. Covered Interest Arbitrage (1)
Covered interest arbitrage is the process of capitalizing on the interest rate differential between two countries while covering for exchange rate risk.
Covered interest arbitrage tends to force a relationship between forward rate premiums and interest rate differentials.
International Financial Management, 2nd edition
Jeff Madura and Roland Fox
ISBN © 2011 Cengage Learning EMEA

9. Covered Interest Arbitrage (2)
Example
£ spot rate = 90-day forward rate = $1.60
U.S. 90-day interest rate = 2%
U.K. 90-day interest rate = 4%
Borrow $ at 3%, or use existing funds which are earning interest at 2%. Convert $ to £ at $1.60/£ and engage in a 90-day forward contract to sell £ at $1.60/£. Lend £ at 4%.
Note: Profits are not achieved instantaneously.
International Financial Management, 2nd edition
Jeff Madura and Roland Fox
ISBN © 2011 Cengage Learning EMEA

10. Covered Interest Arbitrage
Assume you have USD for 90 d
Swiss franc interest rate 4.00% p.a.
US $ interest rate 8.00 % p.a.
Spot rate = CHF/$, 90 day forward = CHF/$
Is arbitrage possible ?

11. Interest Rate Parity

12. Interest Rate Parity

13. Interest Rates and Exchange Rates
A deviation from covered interest arbitrage is uncovered interest arbitrage (UIA). In this case, investors borrow in countries and currencies exhibiting relatively low interest rates and convert the proceed into currencies that offer much higher interest rates.
The transaction is “uncovered” because the investor does no sell the higher yielding currency proceeds forward, choosing to remain uncovered and accept the currency risk of exchanging the higher yield currency into the lower yielding currency at the end of the period.
Assume spotrate for Yen is Y120/$, Yen interest is 0.4% p. a., $ interest is 5 % p.a., Y Expected spotrate in 1 year is also Y120/$

14. Uncovered Interest Arbitrage (UIA): The Yen Carry Trade

15. Interest Rate Parity (IRP)
As a result of market forces, the forward rate differs from the spot rate by an amount that sufficiently offsets the interest rate differential between two currencies.
Then, covered interest arbitrage is no longer feasible, and the equilibrium state achieved is referred to as interest rate parity (IRP).
International Financial Management, 2nd edition
Jeff Madura and Roland Fox
ISBN © 2011 Cengage Learning EMEA

16. Derivation of IRP We use the following symbols
Amount of home currency invested initially is Ah which grows to An after investing in foreign deposit
Spot rate (direct quote) is S and forward rate F
Interest rate is ih at home and if in the foreign country
Return on investing abroad is R

17. Derivation of IRP We have that An = (Ah/S) ● (1+if) ● F
Since F = S ● (1 + p) where p is forward premium, we have that
An = (Ah/S) ● (1+if) ● [S ● (1 + p)]
An = Ah ● (1+if) ● (1 + p)
R = (An – Ah)/Ah

18. Derivation of IRP
For IRP to hold domestic and foreign returns are equal, i.e. R = ih

19. Interest Rate Parity Defined
Or if you prefer,
1 + if
1 + ih = S F
IRP is sometimes approximated as
ih – if = S
F – S

20. Determining the Forward Premium
Example
Suppose 6-month ipeso = 6%, i£ = 5%.
From the U.K. investor’s perspective,
forward premium = 1.05/1.06 – 1 
If S = £.07/peso, then
6-month forward rate = S  (1 + p)
 .07  (1 _ .0094)
 £.06934/peso
International Financial Management, 2nd edition
Jeff Madura and Roland Fox
ISBN © 2011 Cengage Learning EMEA

21. Graphic Analysis of Interest Rate Parity (1)
Interest Rate Differential (%)
home interest rate – foreign interest rate
Forward
Premium (%)
Discount (%)
- 2
- 4 2 4 1 3
- 1
- 3
IRP line Z B X Y A W
International Financial Management, 2nd edition
Jeff Madura and Roland Fox
ISBN © 2011 Cengage Learning EMEA

22. Graphic Analysis of Interest Rate Parity (2)
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
International Financial Management, 2nd edition, Jeff Madura and Roland Fox
ISBN © 2011 Cengage Learning EMEA

23. Test for the Existence of IRP
To test whether IRP exists, collect actual interest rate differentials and forward premiums for various currencies, and plot them on a graph.
IRP holds when covered interest arbitrage is not possible or worthwhile.
International Financial Management, 2nd edition
Jeff Madura and Roland Fox
ISBN © 2011 Cengage Learning EMEA

24. 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.
International Financial Management, 2nd edition
Jeff Madura and Roland Fox
ISBN © 2011 Cengage Learning EMEA

25. Premiums with the US $ and
Does IRP Hold? (1)
Forward Rate
Premiums with the US $ and
Interest Rate
Differentials for
Seven Currencies

26. Does IRP Hold? (2)
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, such as transaction costs, political risk, and differential tax laws.

27. Considerations When Assessing IRP (1)
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
International Financial Management, 2nd edition
Jeff Madura and Roland Fox
ISBN © 2011 Cengage Learning EMEA