Question

The annualized US risk-free rate is 8% and the Germany risk-free rate is 5%. Assume that any period rates less than a year can be interpolated (i.e. if you invested for 6 months then you would receive 4% in the US). The spot quote is €0.80/$ while the 3-month forward quote is €0.7994/$. You can borrow either $1,000,000 or €800,000. According to IRP, is the forward quote correct? If not, what should it be?

If the forward quote is not correct, lay out the steps to implement an arbitrage.

Answer 1

Spot Rate 1 $ = Euro 0.80

3 months fair forward rate = 0.80(1+0.05*3/12)/(1+0.08*3/12)

= 0.80*1.0125/1.02

= Euro 0.7941/$

According to Interest Rate parity, Fair rate is Euro 0.7941/$

Hence, the forward quote is not correct

It should be Euro 0.7941/$

Borrow Euro 800,000

Convert into Dollar and get 800,000/0.80 = $1,000,000

Invest for 3 months and get 1,000,000(1+0.08*3/12)

= $1,020,000

Convert into Euro and get 1,020,000*0.7994 = Euro 815,388

Repay Loan 800,000*(1+0.05*3/12) = 810,000

Arbitrage Profit = Euro 5,388