3. A portfolio manager analyzes 100 stocks and constructs a mean-variance effici

ID: 2777262 • Letter: 3

Question

3. A portfolio manager analyzes 100 stocks and constructs a mean-variance efficient portfolio using these 100 securities. (13 points)

(a) How many estimates are needed to optimize this portfolio? (2 points)

(b) If one could safely assume that stock market returns closely resemble a single-index structure, how many estimates would be needed? (2 points)

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%. Riskfree rate is 4%.

(d) Break down the variance of each stock to the systematic and firm-specific components. (3 points)

(e) What are the covariance and correlation coefficient between the two stocks? (2 points)

(f) What is the covariance between each stock and the market index? (2 points)

3. A portfolio manager analyzes 100 stocks and constructs a mean-variance effici

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