Problem 1. 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 respect to both mean return and volatility, would anyone hold gold? If so, demonstrate graphically why one would do so.
b) Given the data above, reanswer a) with the 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. Could this set of assumptions for expected returns, standard deviations, and correlation represent an equilibrium for the security market?
Problem 2. Consider the following properties of the returns of stock 1, the returns of stock 2 and the returns of the market portfolio (m):
Standard deviation of stock 1 σ1 = 0.30
Standard deviation of stock 2 σ2 = 0.30
Correlation between stock 1 and the market portfolio ρ1, m = 0.2
Correlation between stock 2 and the market portfolio ρ2, m = 0.5
Standard deviation of the market portfolio σm = 0.2
Expected return of stock 1 E (r1) = 0.08
Suppose further that the risk-free rate is 5%.
a) According to the Capital Asset Pricing Model, what should be the expected return on the market portfolio and the expected return of stock 2?
b) Suppose that the correlation between the return of stock 1 and the return of stock 2 is 0.5. What is the expected return, the beta, and the standard deviation of the return of a portfolio that has a 50% investment in stock 1 and a 50% investment in stock 2?
c) Is the portfolio you constructed in part b) an efficient portfolio? Assuming the CAPM is true, could you build a combination of the market portfolio and the portfolio of part b) to increase the expected return of the market portfolio without changing the variance of the combined portfolio.