Assume the U.S. dollar spot exchange rate with the Canadian dollar is $1 = CA$1.125. The U.S. dollar and Swiss Franc exchange rate is $1 = 1.235. If the cross rate between the franc and Canadian dollar is 1 franc = CA$0.9820, then show that an arbitrage is possible. What positions should be taken to profit from the mispricing?

Question

Quizplus · Accepted Answer

CA) To identify arbitrage, calculate the value of transactions through each step. Starting with $1:1. Convert $1 to francs = $1 / 1.235 = 0.8101 francs.2. Convert 0.8101 francs to Canadian dollars = 0.8101 * CA$0.9820 = CA$0.7953.3. Convert CA$0.7953 back to U.S. dollars = CA$0.7953 / 1.125 = $0.7069.This shows a loss, indicating a mistake in my calculation for option A. Let's correct the process:1. Convert $1 to francs = $1 * 1.235 = 1.235 francs.2. Convert 1.235 francs to Canadian dollars = 1.235 * CA$0.9820 = CA$1.2126.3. Convert CA$1.2126 back to U.S. dollars = CA$1.2126 / 1.125 = $1.0778.This corrected calculation shows a profit, indicating an arbitrage opportunity. My initial explanation contained a calculation error. The correct process indeed shows that starting with U.S. dollars, converting to francs, then to Canadian dollars, and back to U.S. dollars results in more U.S. dollars than you started with, confirming arbitrage is possible with option A.C) Let's analyze this option correctly:1. Start with CA$1.2. Convert CA$1 to francs = CA$1 / CA$0.9820 = 1.0183 francs.3. Convert 1.0183 francs to U.S. dollars = 1.0183 / 1.235 = $0.8247.This shows a loss, indicating no arbitrage opportunity for option C. My initial inclusion of option C as a correct answer was incorrect. Upon reevaluation, the correct arbitrage process is described in the corrected explanation for option A, not C. The correct answer is only A, based on the corrected calculations. My initial response mistakenly included C due to a calculation error. The arbitrage opportunity exists by starting with U.S. dollars, converting to francs, then to Canadian dollars, and back to U.S. dollars, as correctly described in the revised explanation for option A.