1. Suppose Southwest Airlinesístock offers an expected return of 10% and a standard deviation of 20%. Suppose American Airlinesístock offers an expected return of 8% and a standard deviation of 16%. The correlation between Americanís stock and Southwestís stock is -0.1. The risk-free rate is 5%.
(a) Graph Capital Allocation Lines (CAL) for Southwest and American on the same graph.
(b) Derive and graph (on the same graph from (a)) the CAL for a risky portfolio created by putting portfolio weights of 0.5 on Southwest and 0.5 on American.
(c) If you can only invest in one of the airlines or the portfolio from (b) along with the risk-free security, which security will a risk averse investor choose? Why?
2. Stocks A, B, and C have the same expected return and standard deviation. The following table shows the correlation coefficients between the returns on these stocks.
Stock A Stock B Stock C
Stock A 1.0.
Stock B 0.9. 1.0
Stock C. 0.1. -0.4. 1.0
Given these correlations, consider the following four portfolios constructed from these stocks. Which portfolio has the lowest risk? Explain.
(a) Equally invested in stocks A and B (b) Equally invested in stocks A and C (c) Equally invested in stocks B and C (d) Totally invested in stock C
3. Stocks offer an expected rate of return of 18%, with a standard deviation of 22%. Gold offers an expected return of 10% with a standard deviation of 30%.
(a) In light of the apparent inferiority of gold with regard to both expected return and standard deviation, would anyone hold gold? If so, demon- strate graphically why one would do so.
(b) Given the information above, re-answer part (a) with an additional assumption that the correlation coefficient between gold and stocks equals 1. Draw a graph illustrating why one would or would not hold gold in one’s portfolio.