Question

Find the one year Futures exchange rate for the Euro.

Spot = $1.12 per Euro

Risk Free Rate in USA = 3%

Risk Free Rate in Europe = 6%

If the 1 year Futures exchange rate is $1.11, what could you do to receive an arbitrage profit?

Answer 1

Given 1Euro = $1.12

As per interest rate parity theory forward rate

=spot rate*[(1+interest rate in US)/(1+interest rate inEuro)]

Forward rate = 1.12*[(1.03)/(1.06)]

= 1.088

Given future price = 1.11

dollar is under priced in future

So arbitrage exists.

Borrow 1000000 dollars @3%

Convert them to Euros using spot rate

= 1000000 / 1.12

= 892857.143 Euros

Invest in Europe @6%

After 1 year you get = 892857.143*(1.06)

= 946,428.572

Convert them to dollars using future rate of 1.11

You get 946,528.572*1.11 = 1,050,535. 71

Loan amount after 1 year = 1000000*1.03 = 1,030,000

After repaying the loan net profit = 1050535.71 - 1030000

$20,535.71