A portfolio manager analyzes 100 stocks and constructs a mean-variance efficient portfolio using these 100 securities.
(a) How many estimates are needed to optimize this portfolio?
(b) If one could safely assume that stock market returns closely resemble a single-index structure, how many estimates would be needed?
Stock C and D are two of these 100 stocks. The index model for these two stocks is estimated from excess return with the following results:
Stock Expected Return Beta Firm-Specific Standard Deviation
C 12% .60 24%
D 20% 1.10 35%
The market index has an expected return of 16% and a standard deviation of 20%. Risk free rate is 4%.
(c) Calculate alpha values for two stocks.
(d) Break down the variance of each stock to the systematic and firm-specific components.
(e) What are the covariance and correlation coefficient between the two stocks?
(f) What is the covariance between each stock and the market index?