# Financial Engineering A1 A portfolio manager expects to purchase a portfolio of stocks in 90 days.

Financial Engineering

A1 A portfolio manager expects to purchase a portfolio of stocks in 90 days. In order to hedge against a potential price increase over the next 90 days, she decide to take a long position on a 90-day forward contract on the S&P 500 stock index. The index is currently at 1145. The continuously compounded divied yield is 1.75% . The risk-free rate is 4.25%.

a) Calculate the non-arbitrage forward price on this contract. b) It is now 28 days since the portfolio manager entered the forward contract. The index value is at 1225. Calculate the value of the forward contract 28 days into the contract. c) At expiration, the index value is 1235. Calculate the value of the forward contract 28 days into the contract.

A2 Consider a U.S.-based company that exports goods to Switzerland. The U.S. Company expects to receive payment on a shipment of goods in three months. Because the payment will be in Swiss francs, the U.S. Company wants to hedge against a decline in the value of the Swiss franc over the next three months. The U.S. risk-free rate is 2 percent, and the Swiss risk-free rate is 5 percent. Assume that interest rates are expected to remain ﬁxed over the next six months. The current spot rate is \$0.5974

a) Indicate whether the U.S. Company should use a long or short forward contract to hedge currency risk. b) Calculate the no-arbitrage price at which the U.S. Company could enter into a forward contract that expires in three months. c) It is now 30 days since the U.S. Company entered into the forward contract. The spot rate is \$0.55. Interest rates are the same as before. Calculate the value of the U.S. Companys forward position.

A3 Suppose that you are a U.S.-based importer of goods from the United Kingdom. You expect the value of the pound to increase against the U.S. dollar over the next 30 days. You will be making payment on a shipment of imported goods in 30 days and want to hedge your currency exposure. The U.S. risk-free rate is 5.5 percent, and the U.K. risk-free rate is 4.5 percent. These rates are expected to remain unchanged over the next month. The current spot rate is \$1.50.

a) Indicate whether you should use a long or short forward contract to hedge currency risk. b) Calculate the no-arbitrage price at which you could enter into a forward contract that expires in three months. c) Move forward 10 days. The spot rate is \$1.53. Interest rates are unchanged. Calculate the value of your forward position.