Stock SZ and stock RO, both have a beta of 1.2. The expected return on the market portfolio is 6%, and the risk-free rate is 1%. The standard deviation of the return of SZ is 62%, of RO is 48%, and of the market portfolio is 20%. The correlation between the returns of SZ and RO is 0.19. Answer the following questions, showing all relevant calculations.
a. What is the expected return on each stock according to the CAPM? Briefly comment on the economic intuition that underpins your answer.
b. What is the correlation between each of these stocks and the market portfolio?
c. What are the systematic and idiosyncratic risk of each of these stocks? Express these risks as standard deviations.
d. What weights should investors with mean-variance preferences put on SZ and RO if they want to construct a portfolio with these two securities? Identify these weights, and calculate the portfolio’s expected return according to the CAPM, and the standard deviation of its returns.
e. Compare the Sharpe ratio of the portfolio you constructed in part (d) above with the Sharpe ratio of a portfolio that puts 100% weight on RO and zero on SZ. Discuss your findings.
f. Discuss the advantages associated with index models in the process of portfolio construction. Do index models entail any disadvantages?