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Document Date: November 2, 2006

An Introduction To Derivatives And Risk Management, 7th

Edition

Don Chance and Robert Brooks

Technical Note: More on Interest Rate Parity, Ch. 10, p. 345

This technical note supports the material in the Foreign Exchange Arbitrage

section of Chapter 10 Futures Arbitrage Strategies. We provide various ways to illustrate

covered interest arbitrage with a numerical example. The basic information is as follows:

Suppose the U. S. interest rate for the next year months is 1.5 percent (annual rate). The

euro interest rate is 2 percent (annual rate). The spot price of the euros in dollars is

$1.665/. The futures price is $1.664/.

Covered interest arbitrage superior rate of return approach

Based on interest rate parity, the correct futures price is given by

( )( )

( )T

T

001

r1STf

+

+= = 1.665(1.015)/(1.02) = 1.6568.

Because the market futures price ($1.664/) is higher than the model price ($1.6568/),

we will sell the futures contract. Simultaneously, we will buy the foreign currency in the

spot market at $1.665/ and sell it in the futures market at $1.664/. We will earn interest

at the foreign interest rate of 2 percent.

By selling futures, we then convert back to dollars at the rate of $1.664/. In

other words, $1.665 would be used to buy 1, which would grow to 1.02 (recall the 2

percent foreign rate). Then 1.02 would be converted back to 1.02($1.664/) =

$1.69728. This would be a return of $1.69728/$1.665 - 1 = 0.019387 or 1.9 percent,

which is better than the U. S. rate of 1.015 percent. Hence, this line of reasoning is

termed the superior rate of return approach. There are a couple of alternative

perspectives of the same arbitrage strategy.

Covered interest arbitrage cash flow table approach

The cash flow table approach is based on illustrating arbitrage profits available

when interest rate parity does not hold. The cash flow table below illustrates the

arbitrage strategy. We assume here the purchase of the foreign currency (euros) would

be financed at the domestic interest rate of 1.5 percent, resulting in a zero net investment.

Remember everything in this table is cash flow and not investment.

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DOMESTIC FOREIGN

2,1t=0US

t=0FC

t=TFC

t=TUS

2,3

1,12,2

We return now to the numerical example. We know the spot foreign exchange

rate is S0 = $1.665/, the domestic interest rate is rDC = 1.5 percent, and the euro rate is

r = 2 percent. To design carry arbitrage, we consider two trading strategies. Strategy 1

is investing $1 in a US bank (1,1). Strategy 2 is investing $1 in a euro-denominated bank

(2,2), first converting the $1 to the (2,1). Also, Strategy 2 requires hedging the foreign

currency risk by selling the appropriate amount of foreign currency at the futures foreign

exchange rate (2,3). Recall the one-year foreign exchange futures price is $1.664/.

These transactions are illustrated below.

IDRM7e, Don M. Chance and Robert-Brooks More on Interest Rate Parity3

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