A portfolio manager holds a $50 million all-equity portfolio with an estimated beta of 1.40. she believes the market will perform strongly over the next three months and decides to use four-month S&P500 futures contracts, which are currently quoted at 2,377.11, to increase the portfolio's exposure to systematic risk. Each futures contract is for the delivery of $250 times the index. The current level of the S&P500 index is 2,371 and it has an estimated dividend yield of 2.1% per annum. The current risk-free interest rate is 1.5% per annum. (a) Calculate the number of futures contracts required to increase the beta of the position to 1.75 over the next three months. Is a long or a short position in the futures required? (1.5 marks) (b) Calculate the total expected value of her position including the futures transactions and the equity portfolio. Assume that the dividend yield on the index and the risk-free rate are expressed as annual rates of interest in your calculations (i.e., similar to what we did in the lecture and tutorial examples). Along the expected value of the overall position, in your answer be sure to state (5 marks): (i) The expected return on the equity portfolio over the next three months. (ii) The expected value of the equity portfolio in three months. The gain/loss on the futures position after three months. (c) What is the return on the portfolio manager's overall position over the next three months? Comment on this value and the outcome of the strategy. (1.5 marks) (iii) A portfolio manager holds a $50 million all-equity portfolio with an estimated beta of 1.40. she believes the market will perform strongly over the next three months and decides to use four-month S&P500 futures contracts, which are currently quoted at 2,377.11, to increase the portfolio's exposure to systematic risk. Each futures contract is for the delivery of $250 times the index. The current level of the S&P500 index is 2,371 and it has an estimated dividend yield of 2.1% per annum. The current risk-free interest rate is 1.5% per annum. (a) Calculate the number of futures contracts required to increase the beta of the position to 1.75 over the next three months. Is a long or a short position in the futures required? (1.5 marks) (b) Calculate the total expected value of her position including the futures transactions and the equity portfolio. Assume that the dividend yield on the index and the risk-free rate are expressed as annual rates of interest in your calculations (i.e., similar to what we did in the lecture and tutorial examples). Along the expected value of the overall position, in your answer be sure to state (5 marks): (i) The expected return on the equity portfolio over the next three months. (ii) The expected value of the equity portfolio in three months. The gain/loss on the futures position after three months. (c) What is the return on the portfolio manager's overall position over the next three months? Comment on this value and the outcome of the strategy. (1.5 marks) (iii)
