Question

1. Interest rates are 10% and 4% per annum in Canada and Switzerland, respectively. The current spot exchange rate ($/SF_r) is 0.3864.

• What is the appropriate one-year forward rate if interest rate parity holds?
• Is there an arbitrage opportunity if the 90-day Swiss francs are quoted at $0.3902/SF_r?

Clearly specify the steps you will take to lock in the arbitrage profit. Validate your arguments with the given data.

Answer 1

1st part:

Spot(S) $/SFr = 0.3864

Interest rate in Canada (i$)=10%

Interest rate in Switzerland(iSFr)=4%

According to Interest rate parity Equation:

F=S * (1+i$)/(1+iSFr)

F=0.3864* (1.1/1.04)+ =0.4087

The 1 year Forward $/SF r= 0.4087

2nd part:

90 day i$=10%*(90/360)=2.5%

90 day iSFr=4%*(90/360)=1%

According to Interest rate parity Equation:

F=S * (1+i$)/(1+iSFr)

F=0.3864* (1.025/1.01) =0.3921

So the 90 Day Forward $/SFr should be = 0.3921 but it is quoted at $0.3902/SFr. Hence there is an arbitrage opportunity.

Steps for arbitrage with an amount of $10000

Step 1: Borrow SFr 10000 for 90 days and calculate amount payable on maturity

Amount payable on maturity=SFr 10000*4%*(90/360) =SFr 10100 ......................(A)

Step 2: Covert SFr 10000 into spot at $/SFr=0.3864 = 10000*0.3864= $3864

Step 3: Invest $3864 & calculate amount receivable on maturity

Amount receivable on maturity=$3864*10%*(90/360)= $3960.6

Step 4: Sell $3960.6 forward at $0.3902/SFR = 3960.6/0.3902 =SFr 10150.18..................(B)

There fore, Arbitrage profit = (B) - (A) = SFr (10150.18 - 10100 ) = SFr 50.18