CAS Exam 9 Spring 2018, Question 1

Study guide: Exam 9

A portfolio manager is looking to make recommendations to his clients using the Capital Asset Pricing Model (CAPM). The research department has developed the following information:

• Investor preference is given by the following utility formula: U = E(r) - \frac{1}{2}A\sigma^2.
• Investor preference for Stock Z is -0.049 for a risk-averse investor.
• The correlation between Stocks X and Y is 0.6.
• The CAPM expected return for Stock X is 12.2%.
• The implied alpha for Stock Y is 2.2%.
• The Sharpe ratios for Stock X and Stock Z are 0.40 and 0.25, respectively.

Part a (4.25 points)

Using CAPM, compare and contrast which stock the portfolio manager would recommend to an investor holding a single stock portfolio versus an investor considering adding one of these stocks to an already well-diversified portfolio. For the single stock portfolio recommended, demonstrate that the risk-reward tradeoff is a better alternative than investing in the market index.

Part b (2.25 points)

For both a risk-averse investor and a risk-neutral investor, justify which stock each would select.

Part c (2 points)

Graph the capital market line, the efficient frontier, the market index, and Stocks X, Y, and Z. Label the axes and all data points. Briefly explain why Stock X cannot lie on the efficient frontier. Explain how the portfolio manager would interpret the perceived value of the price for Stock Y.

Part d (2.5 points)

Demonstrate that the insurance principle of diversification is achieved for the minimum-variance portfolio comprised only of Stocks X and Y.

No current syllabus covers this question; it is kept for the record.

Answer this question and see the worked solution

Concepts tested

• Portfolio
• Cost of Capital
• Covariance
• Standard Deviation

More questions from this set

• CAS Exam 9 Spring 2018, Question 2