Question

ohn is a exchange banker in San Francisco. He is faced with the following market rates:

Spot exchange rate: swiss F 0.9525/$. In other words, 1 US dollar = 0.9525 Swiss f
6 month US dollar interest rate = 0.80% per annum
6 month Swiss franc interest rate = 0.15% per annum
6 month forward exchange rate: = Sfr 0.9445/$

The maximum amount he can borrow and/or invest is $10,000,000 or its equivalent in Swiss francs.

a) Is there a covered interest arbitrage opportunity? Explain why or why not.

b) - Which currency and how much of it would John borrow? Which currency and how much John invest?
- What is the forward transaction John would engage in? Specify which currency and what quantity of that currency he would sell forward and which currency and what quantity of it he would buy forward.
- What is the amount of arbitrage profits? Clearly explain your calculations in words.

For (b) explain the actions you would take to profit from this situation. Your response should include step-by-step verbal explanations as well as detailed calculations.

Answer 1

a]

arbitrage-free forward exchange rate = spot exchange rate * ((1 + Swiss interest rate) / (1 + US interest rate))^6/12

arbitrage-free forward exchange rate = 0.9525 * ((1 + 0.15%) / (1 + 0.80%))^6/12 = SF 0.9494 / $

However, the actual forward exchange rate is SF 0.9454 / $

Hence, there is an arbitrage opportunity

b]

An arbitrage opportunity can be earned with these steps :

• Borrow $10,000,000 at the US interest rate of 0.80% for 6 months. Convert into SF at the spot exchange rate. SF received = 10,000,000 * 0.9525 = SF 9,252,000
• Invest SF 9,252,000 at the Swiss interest rate for 6 months. SF received after 6 months =  SF 9,252,000 * (1 + 0.15%) * (6/12) = SF 9,532,143.75
• Enter into a forward contract today to exchange SF 9,532,143.75 into $ after 6 months. Exercise the forward contract after 6 months. $ received after 6 months = 9,532,143.75 / 0.9445 = $10,092,264.43
• Repay the original $ borrowed. $ to repay = $10,000,000 * (1 + 0.80%) * (6/12) = $10,040,000
• Arbitrage profit = $ received after 6 months - $ to repay after 6 months
• Arbitrage profit = $10,092,264.43 - $10,040,000 = $52,264.43