CAS Exam 9 Spring 2019, Question 3
Study guide: Exam 9
Given the following information about an optimal risky portfolio constructed using a Single Index Model:
- There are 6 stocks in the active portfolio
- For the 6 stocks,
\sum_{i=1}^{6} \left(\frac{\alpha_i}{\sigma^2(e_i)}\right) = 0.5587 \beta_{Active} = 1.0201\alpha_{Active} = 0.0202\sigma^2(e_{Active}) = 0.0362- Short positions are allowed
- The passive portfolio has an expected risk premium of 0.065 and a standard deviation of 0.1494
A 7th stock, Stock G, will be added to the active portfolio to create a new optimal risky portfolio.
A linear regression was performed on excess returns of the Market (independent variable) vs. the excess returns of Stock G (dependent variable). The regression produced the following results:
- Slope = 1.5948
- Standard Deviation of Residual (annualized) = 0.1931
For stock G, assume:
- Annual forecasted alpha = -0.008
- Annual standard deviation = 0.3067
Part a (0.5 points)
Calculate the systematic and non-systematic components of Stock G's variance.
Part b (1.75 points)
Calculate the weight of the active portfolio in the new optimal risky portfolio, including Stock G.
Part c (1 point)
Identify and briefly describe one advantage and one disadvantage of the Single Index Model in comparison with the Markowitz Model.
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