Covered Interest Arbitrage The spot and 360-day forward rates on the Swiss franc are SF 2.1 and SF 1.9, respectively. The risk-free interest rate in the United States is 6 percent, and the risk-free rate in Switzerland is 4 percent. Is there an arbitrage opportunity here? How would you exploit it?

Question

Covered Interest Arbitrage The spot and 360-day forward rates on the Swiss franc are SF 2.1 and SF 1.9, respectively. The risk-free interest rate in the United States is 6 percent, and the risk-free rate in Switzerland is 4 percent. Is there an arbitrage opportunity here? How would you exploit it?

Accepted Answer

Based on interest rate parity, the forward rate should be (approximately):

[latex] F_{1}=S_{0} imes [1+(R_{FC}- R_{US})][/latex]

[latex] =2.1 imes [1+(.04-.06)][/latex]

[latex] =2.06 [/latex]

Because the forward rate is actually SF 1.9, there is an arbitrage opportunity. To exploit the arbitrage opportunity, you first note that dollars are selling for SF 1.9 each in the forward market. Based on IRP, this is too cheap because they should be selling for SF 2.06. So you want to arrange to buy dollars with Swiss francs in the forward market. To do this, you can:

Today: Borrow, say, $1 million for 360 days. Convert it to SF 2.1 million in the spot market, and buy a forward contract at SF 1.9 to convert it back to dollars in 360 days. Invest the SF 2.1 million at 4 percent.
In one year: Your investment has grown to SF 2.1 million × 1.04 = SF 2.184 million. Convert this to dollars at the rate of SF 1.9 = $1. You will have SF 2.184 million / 1.9 = $1,149,474. Pay off your loan with 6 percent interest at a cost of $1 million × 1.06 = $1,060,000 and pocket the difference of $89,474.

Question 21.S-TP.2: Covered Interest Arbitrage The spot and 360-day forward rate...

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