Question: 3. Index Model. [30 Marks] Using the Single-Index Model, a security analyst has obtained the following estimates for stock A and stock B: Stock Alpha

3. Index Model. [30 Marks] Using the Single-Index Model, a security analyst has obtained the following estimates for stock A and stock B: Stock Alpha Beta Firm-specific standard deviation A 3.8% 0.8 30% B 4.2% 1.2 40% ECO-30053 Investment Management 517 The analyst also estimates that the market portfolio has an expected return of 10% and a standard deviation of 22%. The risk-free rate is 6%. 1) Based on the Single-Index Model, what are the systematic risk of stock A and stock B? What are the standard deviations of stock A and stock B? [8 Marks] 2) Calculate the covariance and the correlation coefficient between the two stocks. [4 Marks] 3) Calculate the covariance between each stock and the market index? [2 Marks] 4) Suppose that we construct a portfolio W with 70% of proportion in stock A and 30% of proportion in stock B. Compute the following of portfolio W: a) the excess return, b) beta. c) the firm-specific standard deviation, d) the standard deviation. [8 Marks] 5) Why do we call alpha a "nonmarket" risk premium? Why are high-alpha stocks desirable investments for active portfolio managers? With all other parameters held fixed, what would happen to a portfolio's Sharpe ratio as the alpha of its component securities increased? [8 Marks]

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