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##### [solution] » 1. Suppose that the index model for stocks A and B is estimated

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1. Suppose that the index model for stocks A and B is estimated**More:**

**1. Suppose that the index model for stocks A and B is estimated from excess returns with the following results: **

**RA = 3.4% + 1.15RM + eA**

**RB = ?1.5% + 1.30RM + eB**

**?M = 15.0%; R-squareA = 0.26; R-squareB = 0.16 **

**What is the covariance between each stock and the market index?**

**1. STOCK A**

**2. STOCK B**

**2. Suppose that the index model for stocks A and B is estimated from excess returns with the following results:**

**RA = 3% + 1.00RM + eA**

**RB = ?1.0% + 1.30RM + eB**

**?M = 18%; R-squareA = 0.27; R-squareB = 0.13**

**What are the covariance and correlation coefficient between the two stocks?**

**3.Consider the two (excess return) index model regression results for A and B:**

**RA = 1.5% + 1.7RM R-square = 0.622**

**Residual standard deviation = 12%**

**RB = ?2.4% + 1.3RM R-square = 0.468 Residual standard deviation = 9.8%**

**a. Which stock has more firm-specific risk? Stock A Stock B**

**b. Which stock has greater market risk? Stock A Stock B**

**c. For which stock does market movement has a greater fraction of return variability? Stock A Stock B**

**d. If rf were constant at 5.5% and the regression had been run using total rather than excess returns, what would have been the regression intercept for stock A?**

**4. A portfolio management organization analyzes 54 stocks and constructs a mean-variance efficient portfolio using only these 54 securities. **

**a. How many estimates of expected returns, variances, and covariances are needed to optimize this portfolio? Estimates of expected returns Estimates of variances Estimates of covariances Total estimates**

**b. If one could safely assume that stock market returns closely resemble a single-index structure, how many estimates would be needed? Estimates**

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This question was answered on: * Feb 21, 2020 *

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