You are given the following information about stock X and the market portfolio, M: E(r) Riskless Asset (f) 0.04 (4%) 0.00 Stock X ? 0.30 Market Portfolio (M) 0.10 0.20 You are not given the expected return of stock X. The correlation of the returns on the stock X and the market portfolio is equal to 0.4. a) What is the beta () of stock X? b) Assuming the CAPM holds, what is the expected return on stock X? c) You have $1,000 to invest in some combination of the risk-free asset, stock X, and the market portfolio. You are thinking of investing $300 in the risk free asset, $400 in stock X, and $300 in the market portfolio. What is the overall expected return, standard deviation and beta of this portfolio? d) Instead of making the investment described in part c), you decide to be a little more sophisticated. You are willing to accept an overall standard deviation on your investment of up to 30%, so you decide to invest your $1,000 in whatever combination of the risk-free asset, stock X, and the market portfolio gives you the highest possible expected return, given a standard deviation of 30%? How much money do you invest in each of the three securities, and what is the expected return you achieve? You can assume that stock X is part of the market portfolio.

Suppose it is the start of year 2008. You have $100,000 to invest and decide to invest in a com- bination of a riskless asset (), a stock index fund (S) and a long-term bond fund (B), with the following properties: E(r) 10 Riskless Asset (S) 0.03 (3%) 0.00 Stock index fund (S) 0.12 0.19 Long-term bond fund (B) 0.055 0.10 The correlation of the returns on the long-term bond fund and the stock index fund is equal to 0.3. a) If you only consider the risky assets, what is the global minimum variance portfolio? What is the global minimum variance portfolio if you also consider the risk-free asset?. b) What is the tangency portfolio (i.e., mix) of the risky assets S and B? Hint: You cah figure this out by using Solver in Excel update the Excel spreadsheet from class with the information in the table, define the slope of the CAL, and maximize it. c) What dollar amounts should be invested in each of the three asset classes f, S, and B if you would like to achieve (for the year 2008) an expected return of 8% with the lowest possible standard deviation? What is the standard deviation of the (percentage) return on this portfolio? d) for the year 2008, the realized return on f was 0.03 (3%), the realized return on B was 0.10 (10%) and the realized return on S was -0.40 (-40%). At the end of 2008, what are your dollar holdings off, of B and of S, and how much money do you have in total? What is your realized (percentage) portfolio return for year 2008? Suppose it is the start of year 2008. You have $100,000 to invest and decide to invest in a com- bination of a riskless asset (), a stock index fund (S) and a long-term bond fund (B), with the following properties: E(r) 10 Riskless Asset (S) 0.03 (3%) 0.00 Stock index fund (S) 0.12 0.19 Long-term bond fund (B) 0.055 0.10 The correlation of the returns on the long-term bond fund and the stock index fund is equal to 0.3. a) If you only consider the risky assets, what is the global minimum variance portfolio? What is the global minimum variance portfolio if you also consider the risk-free asset?. b) What is the tangency portfolio (i.e., mix) of the risky assets S and B? Hint: You cah figure this out by using Solver in Excel update the Excel spreadsheet from class with the information in the table, define the slope of the CAL, and maximize it. c) What dollar amounts should be invested in each of the three asset classes f, S, and B if you would like to achieve (for the year 2008) an expected return of 8% with the lowest possible standard deviation? What is the standard deviation of the (percentage) return on this portfolio? d) for the year 2008, the realized return on f was 0.03 (3%), the realized return on B was 0.10 (10%) and the realized return on S was -0.40 (-40%). At the end of 2008, what are your dollar holdings off, of B and of S, and how much money do you have in total? What is your realized (percentage) portfolio return for year 2008