FrmExamen2013Sem1

# FrmExamen2013Sem1 - Question I(Total 10 marks You are long...

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Question I (Total: 10 marks) You are long of a portfolio with value P = 10000 and beta β = 0 . 9 . You want to hedge against price fluctuations using futures written on the index. The index is equal to S 0 = 1 and the dividend yield on the index is 4% per annum. The risk free rate is 3% per annum. The futures price with maturity 6 months is F 0 = 1 . 05 and a futures contract is written on 200 times the futures price. 1. Do you take a short or a long position on the futures market? (justify your answer) . (2 marks) 2. How many contracts do you need to enter into in order to hedge (either long or short according to your previous answer)? (4 marks) 3. At the end of 3 months, the 3-month futures price is 1 . 2 , the spot index is 1 . 1 . We recall the CAPM formula: ExpectedReturnPortfolio = RiskFreeRate + β ( ReturnOnIndex - RiskFreeRate ) We suppose that the portfolio return is equal to “ExpectedReturnPortfolio” given by the above for- mula. Compute your global position at this date. (4 marks) Question II (Total: 10 marks) We have an asset whose value a time t = 0 is S 0 = 1 . This asset pays a dividend of 0 . 05\$ in 2 months. The rate is r = 0 . 04 (CC). 1. What is the 5-month forward price? (2 marks) 2. At time t = 0 you enter into a long forward contract of the previous question, how much does it cost? . (2 mark) 3. Three months later the spot price is 0.9 and rate is still 4% what is the value of your long position at this date? . (2 marks) 4. Suppose that we are at time t = 0 and the 5-month forward price is equal to 0.90. Build explicitly the arbitrage opportunity. (4 marks) Question III (Total: 10 marks) Given two currencies AUD and NZD. The zero-coupon rate curve (CC) for the AUD currency is flat at 4% . The zero-coupon rate curve (CC) for the NZD currency is flat at 5 . 0% . To buy/sell 1 NZD you pay/receive 0.92 AUD.

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