Problem 2 You are discussing your retirement plan with Emma Li when she mentions that Maureen O'Brien, a representative from Toronto Financial Services, is visiting your office today. You decide that you should meet with Maureen, so Emma sets up an appointment for you later in the day. When you sit down with Maureen, she discusses the various investment options available in the company's retirement plan. You mention to Maureen that you researched your new employer before you accepted your new job. Analysis of the company has led to your belief that the company is growing and will achieve a grater market share in the future. You also feel you should support your employer. Given these considerations, along with the fact that you are a conservative investor, you are leaning toward investing 100% of your retirement amount in the company you now work for. Assume the risk-free rate is the historical average T-Bill rate of 3.4%. The correlation between the TO Large-Cap Stock Fund and the TO Bond Fund is 0.1. Note that the spreadsheet graphing and "Solver" in Excel may assist you in answering the questions. 1. How should Maureen respond to the suggestion that you invest 100 percent of your retirement savings in the company you now work for? What about when you say that you are a conservative investor and that a 100 percent investment in the bond fund may be the best alternative. Is it? (1 point) 2. Using the average returns and standard deviations for the TO Large-Cap Stock Fund and the TO Bond Fund (see the table in Problem 1), graph the opportunity set of feasible portfolios you can form from these two risky assets. Examining the opportunity set, notice there is a portfolio that has the lowest standard deviation. What are the portfolio weights, expected return, and standard deviation of this minimum variance portfolio? Why is the minimum variance portfolio important? (1 point) 3. After examining the opportunity set, you notice that you can invest in a portfolio consisting of the bond fund and the large-cap stock fund that will have exactly the same standard deviation as the bond fund. This portfolio will also have a greater expected return. What are the portfolio weights and the expected return of this portfolio? (1 point) 4. What are the portfolio weights, expected return, and standard deviation of the tan- gency portfolio? Using this information graph the capital allocation line alongside the opportunity set of risky assets. How does the Sharpe ratio of the tangency portfolio compare to the Sharpe ratios of the bond fund and the large-cap stock fund? (1 point) 5. Compute an efficient portfolio of both risky funds and a risk-free asset that would be preferred by an investor that has a low volatility (risk) target of o(Rp) = 5%. What is the optimal portfolio for this investor? What about a more risk tolerant investor who has a high expected return target of E(Rp) = 12%. What is the optimal portfolio for this other investor? Report the composition, the expected return, and the volatility of these two portfolios. Comment on the ratio of investment in the TO Large-Cap Stock Fund and the TO Bond Fund for both investors. (2 points) 6. Would some other investors who are considering investing in the TO Large-Cap Stock Fund, the TO Bond Fund, and the risk-free asset find it efficient to short sell only one of the two risky funds? Explain. (1 point) The standard deviation and average return of the funds over the past 10 years: 10-year average return Standard deviation TO TSX Composite Index Fund 9.18% 20.43% TO Small-Cap Stock Fund 14.12% 25.13% TO Large-Cap Stock Fund 8.58% 23.82% TO Bond Fund 5.45% 9.85% Problem 2 You are discussing your retirement plan with Emma Li when she mentions that Maureen O'Brien, a representative from Toronto Financial Services, is visiting your office today. You decide that you should meet with Maureen, so Emma sets up an appointment for you later in the day. When you sit down with Maureen, she discusses the various investment options available in the company's retirement plan. You mention to Maureen that you researched your new employer before you accepted your new job. Analysis of the company has led to your belief that the company is growing and will achieve a grater market share in the future. You also feel you should support your employer. Given these considerations, along with the fact that you are a conservative investor, you are leaning toward investing 100% of your retirement amount in the company you now work for. Assume the risk-free rate is the historical average T-Bill rate of 3.4%. The correlation between the TO Large-Cap Stock Fund and the TO Bond Fund is 0.1. Note that the spreadsheet graphing and "Solver" in Excel may assist you in answering the questions. 1. How should Maureen respond to the suggestion that you invest 100 percent of your retirement savings in the company you now work for? What about when you say that you are a conservative investor and that a 100 percent investment in the bond fund may be the best alternative. Is it? (1 point) 2. Using the average returns and standard deviations for the TO Large-Cap Stock Fund and the TO Bond Fund (see the table in Problem 1), graph the opportunity set of feasible portfolios you can form from these two risky assets. Examining the opportunity set, notice there is a portfolio that has the lowest standard deviation. What are the portfolio weights, expected return, and standard deviation of this minimum variance portfolio? Why is the minimum variance portfolio important? (1 point) 3. After examining the opportunity set, you notice that you can invest in a portfolio consisting of the bond fund and the large-cap stock fund that will have exactly the same standard deviation as the bond fund. This portfolio will also have a greater expected return. What are the portfolio weights and the expected return of this portfolio? (1 point) 4. What are the portfolio weights, expected return, and standard deviation of the tan- gency portfolio? Using this information graph the capital allocation line alongside the opportunity set of risky assets. How does the Sharpe ratio of the tangency portfolio compare to the Sharpe ratios of the bond fund and the large-cap stock fund? (1 point) 5. Compute an efficient portfolio of both risky funds and a risk-free asset that would be preferred by an investor that has a low volatility (risk) target of o(Rp) = 5%. What is the optimal portfolio for this investor? What about a more risk tolerant investor who has a high expected return target of E(Rp) = 12%. What is the optimal portfolio for this other investor? Report the composition, the expected return, and the volatility of these two portfolios. Comment on the ratio of investment in the TO Large-Cap Stock Fund and the TO Bond Fund for both investors. (2 points) 6. Would some other investors who are considering investing in the TO Large-Cap Stock Fund, the TO Bond Fund, and the risk-free asset find it efficient to short sell only one of the two risky funds? Explain. (1 point) The standard deviation and average return of the funds over the past 10 years: 10-year average return Standard deviation TO TSX Composite Index Fund 9.18% 20.43% TO Small-Cap Stock Fund 14.12% 25.13% TO Large-Cap Stock Fund 8.58% 23.82% TO Bond Fund 5.45% 9.85%
