1. International Arbitrage And Interest Rate Parity7
Chapter
International Arbitrage And Interest Rate Parity

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 the various forms of international arbitrage; and
To explain the concept of interest rate parity, and how it prevents arbitrage opportunities.

3. International Parity Conditions
Some fundamental questions managers of MNEs, international portfolio investors, importers, exporters and government officials must deal with every day are:
What are the determinants of exchange rates?
Are changes in exchange rates predictable?
The economic theories that link exchange rates, price levels, and interest rates together are called international parity conditions.
These international parity conditions form the core of the financial theory that is unique to international finance.
In this chapter, we will look at one of the parity conditions, i.e. interest rate parity

4. Prices and Exchange Rates
If the identical product or service can be:
sold in two different markets; and
no restrictions exist on the sale; and
transportation costs of moving the product between markets are equal, then
the products price should be the same in both markets.
This is called the law of one price.
If the law of one price does not hold, arbitrage may become possible

5. International Arbitrage
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.

6. International Arbitrage
As applied to foreign exchange and international money markets, arbitrage takes three common forms:
locational arbitrage
triangular arbitrage
covered interest arbitrage

7. 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
North Bid Ask South Bid Ask
NZ$ £0.37 £0.38 NZ$ £0.39 £0.41
Buy NZ$ from £0.38, and sell it to £0.39. Profit = £0.01/NZ$.

8. Triangular arbitrage
Currency cross rates - ”calculated exchange rates”
Assume 1 £ is worth $ 1.60 and 1 C$ is worth $ 0.80
Cross rate C$/£ = 1.60/0.80 = 2.00
Triangular arbitrage or intermarket arbitrage is possible when a quoted cross exchange rate differs from that calculated using the appropriate spot rates.

9. Triangular arbitrage 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

10. Triangular arbitrage

11. Interest Rates and Exchange Rates
The theory of Interest Rate Parity (IRP) provides the linkage between the foreign exchange markets and the international money markets.
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.

12. Interest Rates and Exchange Rates
The spot and forward exchange rates are not, however, constantly in the state of equilibrium described by interest rate parity.
When the market is not in equilibrium, the potential for “risk-less” or arbitrage profit exists.
The arbitrager will exploit the imbalance by investing in whichever currency offers the higher return on a covered basis.
This is known as covered interest arbitrage (CIA).

13. International Arbitrage
Covered interest arbitrage tends to force a relationship between the interest rates of two countries and their forward exchange rate.
Assume you have £ at your disposal
Spot rate is £0.625/$, 90 day forward £0.625/$
90 day interest rate in US and UK: 2 % and 4 %
In response to the imbalance in demand and supply resulting from such arbitrage activity, the rates will adjust very quickly.

14. 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 ?

15. Interest Rate Parity

16. Interest Rate Parity

17. Currency Yield Curves and the Forward Premium

18. 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/$

19. Uncovered Interest Arbitrage (UIA): The Yen Carry Trade
In the yen carry trade, the investor borrows Japanese yen at relatively low interest rates, converts the proceeds to another currency such as the U.S. dollar where the funds are invested at a higher interest rate for a term. At the end of the period, the investor exchanges the dollars back to yen to repay the loan, pocketing the difference as arbitrage profit. If the spot rate at the end of the period is roughly the same as at the start, or the yen has fallen in value against the dollar, the investor profits. If, however, the yen were to appreciate versus the dollar over the period, the investment may result in significant loss.

20. 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

21. 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

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

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

24. 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 Z B X Y A W

25. 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

26. 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.

27. 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.

28. Does IRP Hold? Forward Rate Premiums with the US $ and Interest Rate
Differentials for
Seven Currencies

29. 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, such as transaction costs, political risk, and differential tax laws.

30. Interest Rates and Exchange Rates
Some forecasters believe that forward exchange rates are unbiased predictors of future spot exchange rates.
Intuitively this means that the distribution of possible actual spot rates in the future is centered on the forward rate.
Unbiased prediction simply means that the forward rate will, on average, overestimate and underestimate the actual future spot rate in equal frequency and degree.

31. Forward Rate as an Unbiased Predictor for Future Spot Rate