Q-2 (25p) Let us assume that around Dec. 2019, the spot exchange rate between the Swiss...

Q-2 (25p) Let us assume that around Dec. 2019, the spot exchange rate between the Swiss Franc and U.S. dollar was 1.0485 (USD per SWF). Interest rates in the United States and Switzerland were 0.75% and 0.25% per annum, respectively with continuous compounding. Assume also that the four-month forward exchange rate was 1.0630 (US$ per SWF).

Is there an arbitrage opportunity for you to make money? (Hint: Recall how to find no-arbitrage forward price!)

If there is NO arbitrage opportunity, explain WHY?

If there is an arbitrage opportunity, using 1.0m USD or 1.0m SWF, how much arbitrage profit you can have in four-month in USD?

Solutions

Expert Solution

a) The arbitrage-free forward rate = Spot rate * (1+Interest rate in US for 4 months)/((1+Interest rate in Switzerland for 4 months)

The arbitrage-free forward rate = 1.0485*e^(0.0075*4/12) /(e^(0.0025*4/12)) = 1.05025 USD per SWF

However, the forward rate = 1.0630 USD per SWF

Hence, an arbitrage opportunity exists

We convert the 1.0m USD to SWF at the spot rate of 1.0485

We get 1,000,000/1.0485 = 953743.44 SWF

We invest the 953743.44 SWF at a SWF risk-free rate of 0.25% per annum

We enter the forward contract to exchange SWF for USD after 4 months

At the end of 4 months, we get 953743.44*e^(0.0025*4/12) = 954538.56 SWF

We exchange these SWF to USD using the forward contract rate of 1.6030 USD per SWF

We get after 4 months= 954538.56*1.0630 = 1014674.48 USD

Had we not exercised this forward, 1.0m USD would had grown at a risk-free rate of 0.75% per annum

1,000,000*e^(0.0075*4/12) = 1002503.12 USD

Hence, the arbitrage profit = (1014674.48-1002503.12) USD

Hence, the arbitrage profit = 12171.36 USD

jeff jeffy answered 1 year ago

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