AN ANALYST REPORTS THE FOLLOWING FUND INFORMATION TO THE ADVISOR OF...
5.
An analyst reports the following fund information to the advisor of a pension fund that currently invests in
government and corporate bonds and carries a surplus of USD 10 million:
Pension Assets
Pension
Liabilities
Amount (in USD million)
100
90
Expected Annual Growth
6%
7%
Modified Duration
12
10
Annual Volatility of Growth
10%
5%
To evaluate the sufficiency of the fund's surplus, the advisor estimates the possible surplus values at the end
of one year. The advisor assumes that annual returns on assets and the annual growth of the liabilities are
jointly normally distributed and their correlation coefficient is 0.8. The advisor can report that, with a
confidence level of 95%, the surplus value will be greater than or equal to:
a.
USD -11.4 million
b.
USD -8.3 million
c.
USD -1.7 million
d.
USD 0 million
Correct Answer: c
Rationale:
The lower bound of the 95% confidence interval is equal to: Expected Surplus - (95% confidence factor *
Volatility of Surplus). The required variables can be calculated as follows:
Variance of the surplus = 100
2
* 10%
2
+ 90
2
* 5%
2
- 2 * 100 * 90 * 10% * 5% * 0.8 = 48.25
Volatility of the surplus =
√
48.25 = 6.94,
The expected surplus = 100 * 1.06 - 90 * 1.07 = 9.7.
Therefore, the lower bound of the 95% confidence interval = 9.7 - 1.645 * 6.94 = -1.725
Section: Risk Management and Investment Management
Reference:
Philippe Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition, Chapter 17,
“VaR and Risk Budgeting in Investment Management.”
Learning Objective:
Distinguish among the following types of risk: absolute risk, relative risk, policy-mix risk, active
management risk, funding risk, and sponsor risk.
2015 Financial Risk Manager (FRM®) Practice Exam