Question

The spot exchange rate between the US dollar and Swiss franc is $1.056 per franc. Swiss banks pay 2.5 percent (annual) interest on their 180-day (6 months) deposits. On similar deposits, American banks pay 1.5 percent (annual.) Assuming that the 180-day forward rate of Swiss franc is $1.045,

1. Do you see an arbitrage opportunity between these two countries? Briefly explain.
2. If your answer were yes, how you would be able to take advantage from it and how much you would make on $100,000 investment?
3. The arbitrage transactions are expected to be followed by some adjustments in the market which will eventually make the arbitrage opportunity disappear. What kind of adjustment do you expect to see in each of the following?
   1. The US interest rate
   2. The spot exchange rate between the dollar and the Swiss franc
   3. The 6-month forward rate between the dollar and the Swiss franc
   4. The Swiss interest rate

Answer 1

Forward rate = Spot rate x (1 + foreign interest rate) / (1 + domestic interest rate)

Accordingly, Forward Rate = $1.056 x (1 + (1.5%/2))/(1 + (2.5%/2))

= $1.05

Pls note that the we need to appropriately adjust the interest rates for 180 days by dividing by 2.

As the 180-day forward rate of Swiss franc (CHF) is $1.045, there is clearly an arbitrage opportunity.

So, the investment of $100,000 = $100,000/1.056 CHF/$ = CHF 94,696.96

It will become $94,696.96 X 1.045 CHF/$ = CHF 98,958.33 as per 180 day forward rate.

whereas it should be $94,696.96 X 1.05 = $99431.81 as per prevailing interest rates in the US & Switzerland.

So, there would be arbitrage profit of $473.48.

In order to make the arbitrage disappear, Swiss banks should pay higher interest rates whereas US banks may pay lower interest rate or alternatively, the 6-month forward rate can be made $1.05 /CHF to nullify the arbitrage opportunity.