a) You have invested only in the Five Stars Fund, a mutual fund that invests mainly in stocks. At the moment, the Five Stars Fund has an expected return of 32% and a volatility of 20%. Your broker suggests that you add the Omega Fund to your current portfolio. The Omega Fund has an expected return of 20%, a volatility of 30% and a correlation of 0.25 with the Five Stars Fund. Risk-free interest rate is equal to 5%. Calculate the required return on the Omega Fund. (5 marks) ii. Will adding Omega Fund improve your portfolio? (3 marks) b) Suppose you have invested all your capital ($200,000) in a portfolio of one stock only, Facebook. Facebook has an expected return of 18% and a volatility of 35%. You know that the market portfolio has an expected return of 11% and a volatility of 13%. Assume that the risk-free interest rate is 3%. Under the CAPM assumptions: What alternative investment has the lowest possible volatility while having the same expected return as Facebook? What is the volatility of this new portfolio? (4 marks) What investment has the highest possible expected return given that you want to maintain the same volatility as Facebook? What is the expected return of this new portfolio? (4 marks) Question 12 continued f) Suppose that the expected risk premium on small stocks relative to large stocks is 7%, the expected risk premium on high book-to-market stocks relative to low book-to-market stocks is 5%, and the expected risk premium on prior one year momentum portfolio is 4%. Assume that the expected risk premium on the overall stock market relative to the risk-free rate is 8%. Facebook stock has a market beta of 1.3, a size beta of 0.3, a book-to-market beta of 0.2, and a prior one year momentum beta of 0.1. If the risk-free rate is 3%, what is the expected return on Facebook stock according to the F-F-C model? (5 marks) a) You have invested only in the Five Stars Fund, a mutual fund that invests mainly in stocks. At the moment, the Five Stars Fund has an expected return of 32% and a volatility of 20%. Your broker suggests that you add the Omega Fund to your current portfolio. The Omega Fund has an expected return of 20%, a volatility of 30% and a correlation of 0.25 with the Five Stars Fund. Risk-free interest rate is equal to 5%. Calculate the required return on the Omega Fund. (5 marks) ii. Will adding Omega Fund improve your portfolio? (3 marks) b) Suppose you have invested all your capital ($200,000) in a portfolio of one stock only, Facebook. Facebook has an expected return of 18% and a volatility of 35%. You know that the market portfolio has an expected return of 11% and a volatility of 13%. Assume that the risk-free interest rate is 3%. Under the CAPM assumptions: What alternative investment has the lowest possible volatility while having the same expected return as Facebook? What is the volatility of this new portfolio? (4 marks) What investment has the highest possible expected return given that you want to maintain the same volatility as Facebook? What is the expected return of this new portfolio? (4 marks) Question 12 continued f) Suppose that the expected risk premium on small stocks relative to large stocks is 7%, the expected risk premium on high book-to-market stocks relative to low book-to-market stocks is 5%, and the expected risk premium on prior one year momentum portfolio is 4%. Assume that the expected risk premium on the overall stock market relative to the risk-free rate is 8%. Facebook stock has a market beta of 1.3, a size beta of 0.3, a book-to-market beta of 0.2, and a prior one year momentum beta of 0.1. If the risk-free rate is 3%, what is the expected return on Facebook stock according to the F-F-C model
