CAS Exam 9 Spring 2019, Question 2
Study guide: Exam 9
An investor has constructed a portfolio according to the Markowitz Portfolio Optimization Model, from the set of fixed-income securities with the following features:
| Bond | Coupon Frequency | Time to Maturity (years) | Par Value | Price | Current Yield | Yield to Maturity | Macaulay Duration | Portion of Portfolio |
|---|---|---|---|---|---|---|---|---|
| 1 | Annual | 25 | $1,000 | $786.50 | 7.63% | 8% | 12.15 | 43.4% |
| 2 | N/A | 2 | $100 | $92.46 | 0.00% | 20.0% | ||
| 3 | Semi-annual | 5 | $1,000 | $852.80 | 9.38% | 36.6% |
Covariance Matrix:
| Bond | 1 | 2 | 3 |
|---|---|---|---|
| 1 | 0.0144 | 0.0000 | 0.0072 |
| 2 | 0.0000 | 0.0000 | 0.0000 |
| 3 | 0.0072 | 0.0000 | 0.0400 |
Part a (3.25 points)
Calculate the investor's risk aversion index, A.
Part b (1.25 points)
Calculate the (Macaulay) duration of the investor's asset portfolio.
No current syllabus covers this question; it is kept for the record.
Answer this question and see the worked solution