It is now 1 April 2011. The continuous compounded certificate of deposit interes
ID: 2671197 • Letter: I
Question
It is now 1 April 2011. The continuous compounded certificate of depositinterest rate in Switzerland is 6% per annum and it is 4% per annum in
the US. The June Swiss francs futures price is US$0.75 per franc while
the spot exchange rate today is US$0.70 per Swiss franc. The delivery
date for June futures contracts is at the end of June and each contract has
SF100,000.
Outline the steps required to do the arbitrage. Assuming an investor
needs to borrow US$ to make the arbitrage, evaluate the arbitrage
gain in US dollars assuming the spot rate when the futures contract
expires is US$0.75 per Swiss franc using one futures contract.
Explanation / Answer
• Borrow US$70,000 at 4% per annum (continuously compounded) for 3 months. • After 3 months, the investor will have to return: A = Pe^rt r = 4% = 0.04 t = 3/12 = 0.25 year A = 70,000 * e^0.04*0.25 = 70,000 * 1.01005 = $70,704 • Exchange US$70,000 into 70,000 / 0.70 = SF 100,000 • Invest SF 100,000 at 6% per annum (continuously compounded) for 3 months to get: 100,000 * e^0.06*0.25 = 100,000 * 1.015113 = SF 101,511 • Sell SF 101,511 via 3 month future contract, to receive US$76,133 (101,511*0.75) i.e. to exchange Swiss francs back into US dollars in 3 months at today’s future price. • At the expiry of 3 months, he will incur three transactions. 1. First, he will get SF 101,511 from investment. 2. Second, he will exchange SF 101,511 into US$76,133 under future contract. 3. Third, he will return US$70,704 for the money borrowed. • Profit in the process = US$76,133 – US$70,704 = US$5,429
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