14. Continued
(a) (6 points) Calculate VaRs at the 99th percentile on a comparable basis under each
of the following approaches. Show your work.
i. Variance – Covariance
ii. Historical Simulation
iii. Monte Carlo
(b) (2 points) Explain to your client how to interpret VaR and why VaR may vary
using different approaches.
(c) (2 points) Describe the pros and cons of each of the above three VaR approaches.
COURSE 8: Fall 2005 - 15 - STOP
Enterprise Risk Management Segment
Afternoon Session
15. (6 points) Darth Insurance Company is considering selling a one-year segregated fund
maturity guarantee. The underlying fund, Equity Asset Fund, is an index fund whose
returns track the S&P 500.
Data and assumptions associated with this product are:
• Current unit price of Equity Asset Fund: $1,050
• Guaranteed fund value at the end of the year: $1,092
• Risk-Free Rate: 5% per year
• Downward movement nt factor for Equity Asset Fund: d = 0.9
• Upward movement factor for Equity Asset Fund: u = 1.1
• The Equity Asset Fund returns have a lognormal distribution.
(a) Using a one-period binomial tree, determine the composition and value of the
risk-free hedge portfolio at the end of year one. Show your work.
(b) Re-calculate the value of the hedge portfolio at the end of year one assuming
management fees are 1%. Show your work.
(c) Explain why the hedge calculated is unlikely to be completely effective.
**END OF EXAMINATION**
AFTERNOON SESSION