CAS Exam 9 Spring 2016, Question 1
Study guide: Exam 9
An investor has a risk aversion factor of A = 2. The investor has $100,000 to invest in a combination of an S&P 500 index fund and risk-free assets. Given the following information:
- The investor's utility is given by
U = E(r_c) - 0.5A\sigma_c^2. - The investor's risk-free lending rate is 4%.
- The investor's risk-free borrowing rate is 6%.
- The S&P 500 index offers an expected return of 11.5% with a standard deviation of 20%.
Part a (0.5 points)
The investor would like to achieve the greatest possible return, subject to a maximum standard deviation of 25%. Calculate the amount the investor should allocate to risk-free assets.
Part b (0.75 points)
Calculate the expected return and standard deviation of the portfolio in part a. above.
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