International Arbitrage And Interest Rate Parity 7 Chapter International Arbitrage And Interest Rate Parity

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.

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

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

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.

International Arbitrage As applied to foreign exchange and international money markets, arbitrage takes three common forms: 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. Example North Bid Ask South Bid Ask NZ$ £0.37 £0.38 NZ$ £0.39 £0.41 Buy NZ$ from North @ £0.38, and sell it to South @ £0.39. Profit = £0.01/NZ$.

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.

Triangular arbitrage Assume you have the following quotations 1 000 000 $ to play with Westminster Bank: $ 1.5500/£ Shanghai Bank € 1.5000/£ Wells Fargo $ 1.0600/€ Is triangular arbitrage possible ? Cross rate $/€ = 1.55/1.50 = 1.0333 Sell $ where it`s expensive, buy it back where it`s cheap

Triangular arbitrage

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.

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).

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 £ 800 000 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.

Covered Interest Arbitrage Assume you have 1 000 000 USD for 90 d Swiss franc interest rate 4.00% p.a. US $ interest rate 8.00 % p.a. Spot rate = 1.4800 CHF/$, 90 day forward = 1.4655 CHF/$ Is arbitrage possible ?

Interest Rate Parity

Interest Rate Parity

Currency Yield Curves and the Forward Premium

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 10 000 000. Expected spotrate in 1 year is also Y120/$

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.

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

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

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

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

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

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

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.

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? Forward Rate Premiums with the US $ and Interest Rate Differentials for Seven Currencies

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.

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.

Forward Rate as an Unbiased Predictor for Future Spot Rate