Your friend is facing an important decision. She was recently hired by a large bank, XYZ, as a junior associate. Her primary responsibility is reviewing loan applications for completeness and conducting an initial analysis of the credit information. She is very knowledgeable about loans; however, she has come to you with a dilemma. The decision she is facing does not involve a work-related task, rather it involves questions regarding how she should set up her retirement account. She wants to get started investing early in life as she understands the power of compound interest, but she is unclear about where she should allocate her money. She has heard that you have a solid understanding of investments, particularly the risk and return of securities. She has narrowed her options down to three choices and would like your input. The first option is to invest in a mutual fund that is comprised of a wide variety of common stock from large, domestic firms. The second option is to invest in a low-risk government security, such as U.S. Treasury bills (T-bills). The third option is to invest in the common stock of XYZ. Your friend is very worried about losing her money and would like to keep her investment choice simple. For that reason she is considering choosing to invest in XYZ common stock as she has calculated an average return for the stock that seems acceptable. Currently, your friend has $5,000 to invest.

1. Based solely on the information that you have at this point, what advice would you give your friend regarding her choice of investment? What recommendations would you have for her? How would you explain your choice?

2. You have decided to gather more quantitative information about each of the investment choices. You have found that, over the long-term, the risk-free rate is approximately 3.4%. Over that same period of time, you have found that the stock market has averaged a return of 13.1%. The covariance between the common stock mutual fund and the market is 0.01575 and the covariance between XYZ and the market is 0.0285. The variance of the market is 0.015. The beta for the government security is 0. Using the CAPM method, what is the expected return for each of these investment options (you will need to calculate the betas for the mutual fund and XYZ)? How can you explain to your friend why the expected returns of each investment are different?

3. After careful consideration, you believe that your friend should hold a portfolio, rather than a single investment. You recommend investing in both the common stock mutual fund and the government security. You believe that 80% of the portfolio should consist of the mutual fund and 20% should consist of the government security. Based on the calculations you completed in the previous question, what is the expected return of the portfolio? What is the standard deviation of the portfolio if the variance of the mutual fund is 0.076, the variance of the government security is 0.010 (assuming this is the risk-free asset), and the covariance between the mutual fund and the government security is -0.0037? What reasoning could you provide to your friend as to why to have a portfolio rather than just a single investment? Why would you not recommend investing only in the stock of XYZ?

4. Your friend likes the idea of holding both the common stock mutual fund and the government security, but she thinks that your suggestion to hold 80% of the former and 20% of the latter is too risky. She mentions that the maximum level of risk she is willing to assume is a portfolio with a standard deviation of 15%. How would you find a combination that meets this requirement?