Question

Suppose that you’re a FX trader for a bank in New York. You are faced with the following market rates:

Spot exchange rate: Sfr 0.9525/$. In other words, 1 US dollar = 0.9525 Swiss francs

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 you may 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) Continuing with the problem, spell out the actions you would take to profit from this situation. Your response should include step-by-step verbal explanations as well as detailed calculations.

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

Answer 1

As per Interest Rate Parity,

Theoretical Forward Rate Sfr/$ = Spot Sfr/$*(1+Interest Rate on Swiss Franc)/(1+Interest Rate on $)

= 0.9525*[1+(0.0015/2)]/[1+(0.008/2)]

= 0.9494

Actual Forward Rate < Theoretical Forward Rate

As the Rates are different, there is a Covered Interest Arbitrage Opportunity.

Therefore, Actual Forward Rate of $ is Undervalued

To make an Arbitrage Gain, Sell $ in Spot and Buy in Forward

Steps to make an Arbitrage Gain:

Now,

1. Borrow $10000000 for 6 months
2. Buy Sfr at Spot Rate using $10000000 and receive 10000000*0.9525 = Sfr 9525000
3. Invest Sfr 9525000 for 6 months
4. Enter into Forward Contract to Sell 9525000*(1+0.00075) = Sfr 9532143.75

After 6 months,

5. Realize Investments and receive 9525000*(1+0.00075) = Sfr 9532143.75
6. Sell Sfr 9532143.75 under Forward Contract and receive 9532143.75/0.9445 = $10092264.43
7. Repay the borrowings along with interest and pay 10000000*(1+0.004) = $10040000
8. Arbitrage Gain = Difference = $10092264.43 - $10040000 = $52264.43