13.A portfolio manager has a $250m position in an equity portfolio which tracks the CARSON500 index. The manager is concerned about the possibility of a short term fall in the index and consequent decrease in the value of his portfolio. As a result investors may question his or her competence and invest their money elsewhere. To address this issue the fund manager decides to hedge using futures written on the CARSON500 index. The current value of the index is 5,000 points with a continuously compounded dividend yield of 3.5% per annum. The portfolio has a beta of 1.3 with respect to the index. The relevant futures contract has 6 months to maturity and has a contract multiple of $10 per full index point. The risk-free rate of interest is 2.5% per annum. (a) Calculate the futures position required to hedge the portfolio using a beta hedge. (30 marks) (b) After 3 months the spot price of the index falls to 4,500 points and the futures position is closed out. What will be the new quoted futures price, the gain or loss on the futures and spot positions and the return on the hedged portfolio? (40 marks) (c) Discuss whether this is likely to be a perfect hedge. (30 marks) 13.A portfolio manager has a $250m position in an equity portfolio which tracks the CARSON500 index. The manager is concerned about the possibility of a short term fall in the index and consequent decrease in the value of his portfolio. As a result investors may question his or her competence and invest their money elsewhere. To address this issue the fund manager decides to hedge using futures written on the CARSON500 index. The current value of the index is 5,000 points with a continuously compounded dividend yield of 3.5% per annum. The portfolio has a beta of 1.3 with respect to the index. The relevant futures contract has 6 months to maturity and has a contract multiple of $10 per full index point. The risk-free rate of interest is 2.5% per annum. (a) Calculate the futures position required to hedge the portfolio using a beta hedge. (30 marks) (b) After 3 months the spot price of the index falls to 4,500 points and the futures position is closed out. What will be the new quoted futures price, the gain or loss on the futures and spot positions and the return on the hedged portfolio? (40 marks) (c) Discuss whether this is likely to be a perfect hedge. (30 marks)