Chapter 7 International Arbitrage and Interest Rate Policy International Financial Management, 2nd edition Jeff Madura and Roland Fox ISBN 978-1-4080-3229-9 © 2011 Cengage Learning EMEA

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 978-1-4080-3229-9 © 2011 Cengage Learning EMEA

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 978-1-4080-3229-9 © 2011 Cengage Learning EMEA

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 978-1-4080-3229-9 © 2011 Cengage Learning EMEA

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 C @ $0.64, and sell it to Bank D @ $0.645 Profit = $.005/NZ$. International Financial Management, 2nd edition Jeff Madura and Roland Fox ISBN 978-1-4080-3229-9 © 2011 Cengage Learning EMEA

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 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

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 978-1-4080-3229-9 © 2011 Cengage Learning EMEA

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 978-1-4080-3229-9 © 2011 Cengage Learning EMEA

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

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

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 978-1-4080-3229-9 © 2011 Cengage Learning EMEA

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

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  - .0094 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 978-1-4080-3229-9 © 2011 Cengage Learning EMEA

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 978-1-4080-3229-9 © 2011 Cengage Learning EMEA

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 978-1-4080-3229-9 © 2011 Cengage Learning EMEA

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 978-1-4080-3229-9 © 2011 Cengage Learning EMEA

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 978-1-4080-3229-9 © 2011 Cengage Learning EMEA

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

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.

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 978-1-4080-3229-9 © 2011 Cengage Learning EMEA