Question

suppose that the anual intrest rate is 1.5 percent in the united states and 3 percent in germany, and that the spot exchange rate is 1.8 assume tht an arbitrager can borrow up to 1,000,000 or 625,000, if an astute trader finds an arbitrage, what is the arbitrage profit in one year

Answer 1

Suppose, F is the forward foreign exchange rate

As per the Covered Interest formula S*(1+Id)=F*(1+If) (S= spot exchange rate, Id= domestic interest rate, If= foreign interest rate)

So, 1.8*(1+1.5%)=F*(1+3%) or, F= 1.7737

So, At equilibrium at the end of one year the the exchange rate should be 1.7737

Arbitrage opportunity= (1.8-1.7737-0.015) or (0.026-0.015) per dollar -

If he borrow 1,000,000, his profit would be= 1,000,000*0.026- Interest Rate= 26213.6-1000000*1.5%=$11213.59

If he borrows 625000 his profit=625000*0.026-625000*1.5%=$6875