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?