Question

The euro currently trades at $1.0231. The dollar risk-free rate is 4 percent, and the euro risk-free rate is 5 percent. Six-month forward contracts are quoted at a rate of $1.0225. Indicate how you might earn a risk-free profit by engaging in a forward contract. Clearly outline the steps you undertake to earn this risk-free profit.

Answer 1

Implied forward rate is given as = spot rate * (1+interest rate of dollar for 6 months) /(1+interest rate of euro for 6 months)

=1.0231*(1+4%/2)/(1+5%/2)

=1.0231*1.02/1.025

=1.0181

Hence the implied forward rate is lower than current traded forward rate

Now the arbitrage can be done in the following way-

Borrow $1000 at 4% for 6 months

Hence payment after 6 months will be =1000*(1+4%*6/12)=1020

You have to purchase euro at spot

Hence euro purchased=$1000/$1.0231/euro

=euro 977.421

Invest euro at 5% per annum for 6 months hence investment after 6 months will be = 977.421*(1+5%*6/12)

=euro 1001. 857

Now sell euro 1001.857 (sell euro) at a current forward rate of 1.0225

(note = you will recieve 1001.857 from your euro investment in 6 months and hence you are converting euro into dollars after 6 months sellimg euro forward)

Hence the amount you will get after 6 months=euro1001.857*$1.0225/Euro=$1024. 399

Hence inflow after 6 months by trading in forward and delivering euro=$1024.399

Outflow after 6 months for repayment of borrowing in dollar=$1020

Arbitrage profit =1024.399-1020=$4.399