1. Mary decides to set aside a small part of her wealth for investment in a portfolio that has greater risk than her previous investments because she anticipates that the overall market will generate attractive returns in the future. She assumes that she can borrow money at 3% (the risk-free rate) and achieve the same return on the S&P 500 as before: an expected return of 12% with a standard deviation of 22%.
A. Calculate Mary's expected risk and return if she borrows 20%, 60% and 100% of her initial investment. Show your calculations.
B. What is the slope of he capital market line for part A? Show your calculations.
C. Assume that Mary can borrow at 6 percent instead the risk-free rate. What would be the expected return and risk if Ms. Moneypenny borrows 20%, 60% and 100% of her initial investment? Show your calculations.
D. How does the slope of the capital market line change from part A to part C? Explain why the slope of the capital market line changes. Show your calculations.
2. An investor is considering investing in a small-cap stock fund and a general bond fund. The correlation between the returns of the two funds is 0.10. The returns and standard deviations are given in the following table.
|
Expected Annual Return
|
Standard Deviation of Returns
|
|
Emerging Markets stock fund
|
28%
|
40%
|
|
Global Equities Fund
|
16%
|
21%
|
A. If the investor requires a portfolio return of 23 percent, what should the percentage invested in each fund be? Show your calculations.
B. What is the standard deviation of a portfolio constructed according to the weights computed in part A? Show your calculations.