# International Arbitrage and Interest Rate Parity

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International Arbitrage and Interest Rate Parity
CHAPTER 7 International Arbitrage and Interest Rate Parity © 2000 South-Western College Publishing 1

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 Arbitrage
Arbitrage can be defined as capitalizing on a discrepancy in quoted prices. Often, the funds invested are not tied up and no risk is involved. Locational arbitrage is possible when the bid price of one bank is higher than the ask price of another bank for the same currency. e.g Bank A Bank B dollars -> pounds pounds -> dollars \$1.61 / £ \$1.62 / £ In response to the imbalance in demand and supply resulting from such arbitrage activity, the prices will adjust very quickly.

International Arbitrage
Triangular arbitrage is possible when a quoted cross exchange rate differs from that calculated using the appropriate spot rates. e.g. Bank A Bank B Bank C \$ -> £ £ -> Canadian\$ Canadian\$ -> \$ \$1.60 / £ £ / C\$ \$0.81 / C\$ Note: Calculated cross rate = £ / C\$ In response to the imbalance in demand and supply resulting from such arbitrage activity, the prices will adjust very quickly.

International Arbitrage
Covered interest arbitrage tends to force a relationship between the interest rates of two countries and their forward exchange rate. e.g. 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%. In response to the imbalance in demand and supply resulting from such arbitrage activity, the rates will adjust very quickly.

International Arbitrage
Locational arbitrage ensures that quoted exchange rates are similar across banks in different locations. Triangular arbitrage ensures that cross exchange rates are set properly. Covered interest arbitrage ensures that forward exchange rates are set properly. Any discrepancy will trigger arbitrage, which will then eliminate the discrepancy. Arbitrage thus makes the foreign exchange market more orderly.

Interest Rate Parity When market forces cause interest rates and exchange rates to be such that covered interest arbitrage is no longer feasible, the equilibrium state achieved is referred to as interest rate parity (IRP). When IRP exists, the rate of return achieved from covered interest arbitrage should equal the rate available in the home country By simplifying and rearranging terms: forward = (1 + home interest rate) _ 1 premium (1 + foreign interest rate)

Interest Rate Parity If the 6-month Mexican peso interest rate = 6% ,
6-month U.S. dollar interest rate = 5% , then from the U.S. investor’s perspective, forward = ( ) _ 1 = _ .9434% premium ( ) (not annualized) If the peso’s spot rate is \$.10/peso, then the 6-month forward rate = spot rate x (1 + premium) = .10 x (1 _ ) = \$.09906/peso

Interest Rate Parity The relationship between the forward rate and the interest rate differential can be simplified and approximated as follows: forward = forward rate - spot rate premium spot rate » home _ foreign interest rate interest rate This approximated form provides a reasonable estimate when the interest rate differential is small.

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

Graphic Analysis of Interest Rate Parity
Home Interest Rate - Foreign Interest Rate (%) Forward Premium (%) Discount (%) - 2 - 4 2 4 1 3 - 3 - 1 IRP line Zone of potential covered interest arbitrage by foreign investors Zone of potential covered interest arbitrage by local investors Zone where covered interest arbitrage is not feasible

Interest Rate Parity IRP generally holds. Where it does not hold, covered interest arbitrage may still not be worthwhile due to transaction costs, currency restrictions, differential tax laws, political risk, etc. 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.

Correlation Between Spot and Forward Rates
Interest Rates iA iU.S. time Forward Rates Spot and SpotA ForwardA. Because of interest rate parity, a forward rate will normally move in tandem with the spot rate. This correlation depends on interest rate movements.

Impact of Arbitrage on an MNC’s Value
Forces of Arbitrage 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 = the weighted average cost of capital of the U.S. parent

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

Chapter Review Interest Rate Parity Derivation of Interest Rate Parity
Numerical Example Graphic Analysis of Interest Rate Parity Interpretation of Interest Rate Parity Considerations When Assessing Interest Rate Parity Correlation Between Spot and Forward Rates Impact of Arbitrage on an MNC’s Value

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