Question

In early 2012, the spot exchange rate between the Swiss Franc and U.S. dollar was 1.0404 ($ per franc). Interest rates in the United States and Switzerland were 0.25% and 0% per annum, respectively, with continuous compounding. The 3-month forward exchange rate was 1.0300 ($ per franc). What arbitrage strategy was possible? How does your answer change if the forward exchange rate is 1.0500 ($ per franc).

Answer 1

The theoretical forward exchange rate is 1.0404e^{(0.0025−0)×0.25} = 1.041.

Calculating the same using BA 2 Plus Calculator , Use the following steps:

1, Input 1.0404. Click on "STO" and Press "1". This will store the value in 1 so you dont need to put it again and again.

2. Now, let us solve the equation in the numerator (.0025-0)*.25 = .000625. Press "2ND" and press "LN". This gives access to e function.Answer will be 1.000625.

3. Press "x" multiplication sign and then press "RCL" function. (This is used to recall stored value). Press "1" and you will have  1.0404 on screen. Press Equal to and you will get 1.041.

In the first situation [gain through LONG position] , gain using arbitrage strategy = 1.041- 1.03 = .011.

This gain can be achieved by borrowing swiss francs and converting the swiss francs into dollars and investing them at risk free rate for 3 months and buy Swiss francs at 1.03 in the forward market.

In the second situation [gain through SHORT position],  The gain can be achieved by borrowing borrowing dollars , converting the dollars into swiss francs and investing them at risk free rate of 0%. Enter into a forward contract to short 1.0404 swiss francs in three months. The forward contracts convert these to 1.05/1.0404 = 1.0092 USD

e^0.0025×0.25 =1.0006 needs to be repaid for the dollar loan.

This can be calculated on BA 2 plus calculator using the above mentioned steps

Gain = 1.0092-1.0006 = .0086