Question

Suppose the spot and six-month forward rates on the South Korean won are SKW 1,304.99 and SKW 1,314.80, respectively. The annual risk-free rate in the United States is 4 percent, and the annual risk-free rate in South Korea is 5 percent.

What must the six-month forward rate be to prevent arbitrage? (Do not include the South Korean won sign (SKW). Do not round intermediate calculations and round your answer to 4 decimal places, e.g., 32.1616.)

Forward rate            SKW

Answer 1

In the given quotes, domestic currency is U.S. dollars and foreign currency is South Korean won .so, spot exchange rate of SKW 1,304.99 is equal to 1 U.S. dollar.

six-month forward rate to prevent arbitrage = spot exchange rate*[(1+domestic interest rate)/(1+foreign interest rate)]

we need to calculate forward rate for six-month whereas given risk-free rates are annual. so, we will use six-month risk-free rates by dividing annual rates by 2 as there are two six-month periods in a year.

six-month forward rate to prevent arbitrage = SKW 1,304.99*[(1+0.04/2)/(1+0.05/2)] = SKW 1,304.99*[(1+0.02)/(1+0.025)] = SKW 1,304.99*(1.02/1.025) = SKW 1,304.99*0.9951219512195122 = SKW 1,298.6242

the six-month forward rate must be 1,298.6242 to prevent arbitrage.