Question

Suppose that the current exchange rate is SF1.25/$ and three month forward exchange rate is SF1.30/$. The three-month interest rate is 4 percent per annum in United States and 8 percent per annum in Switzerland. Assume that you can borrow up to $1,000,000 or SF 1,250,000.

a) Is Interest Rate Parity holding?

b) If your answer to part a is no, how would you realize a certain profit via a covered interest arbitrage? Also determine the size of the arbitrage profit.

Answer 1

Part (a)

If interest rate parity held true then the three month forward exchange rate should be = Spot rate x (1 + n/12 x i_SF) / (1 + n/12 x i_US) = 1.25 x (1 + 3/12 x 8%) / (1 + 3/12 x 4%) = SF 1.26 / $

However the actual forward rate is SF 1.30 / $

Hence, the interest rate parity is not holding true.

Part (b)

Arbitrage strategy:

• Borrow SF 1,250,000 @ i_SF = 8% for three months; liaiblity on maturity = 1,250,000 x (1 + 8% x 3/12) =  SF 1,275,000
• Convert them into $ = SF 1,000,000 / Spot rate = 1,250,000 / 1.25 = $ 1,000,000
• Enter into a forward contract to sell $ after three months at the rate of SF 1.30 / $
• Lend the $ @ i_US = 4% for three months; maturity proceeds after three months = $ 1,000,000 x (1 + 4% x 3/12) = $ 1,010,000
• On maturity of forward contract, sell the $ to get $ 1,010,000 x 1.30 / $ = SF 1,313,000
• Payoff the obligation of SF 1,275,000 on the borrowed SF at t = 3 months

Arbitrage profit = 1,313,000 - 1,275,000 = SF 38,000