FrmExamen2012Sem2 - 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 = 1 . 1 . 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 5% per annum. The risk free rate is 4% 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 0 . 95 , the spot index is 0 . 9 . We recall the CAPM formula: ExpectedReturnPorfolio = RiskFreeRate + β ( ReturnOnIndex - RiskFreeRate ) We suppose that the portfolio return is equal to “ExpectedReturnPorfolio” given by the above formula. 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 . 06$ in 2 months. The rate is r = 0 . 05 (CC). 1. What is the 4-month forward price? (1.5 marks) 2. At time t = 0 you enter into a long forward contract of the previous question, how much does it cost? . (1 mark) 3. Three months later the spot price is 0.9 and rate is still 5% what is the value of your long position at this date? . (1.5 marks) 4. Suppose that we are at time t = 0 and the 4-month forward price is equal to 0.90. Build explicitly the arbitrage opportunity. (6 marks) 1
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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 0.95 AUD.
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