Sample Questions
Question 1
Easy
In profit testing, the term appears in the profit recursion. What does this term represent?
Solution
A is correct.
The profit recursion tallies all cash outflows at year-end. For each policy that survives to year-end — a fraction of those in force at year-start — the insurer must hold the reserve . The expected total reserve held for survivors is , which is a cash outflow (from the profit perspective) representing the liability being carried forward.
The profit recursion tallies all cash outflows at year-end. For each policy that survives to year-end — a fraction of those in force at year-start — the insurer must hold the reserve . The expected total reserve held for survivors is , which is a cash outflow (from the profit perspective) representing the liability being carried forward.
Question 2
Medium
Year-4 gains: , , ; , , fund ; , . Compute total gain.
Solution
B is correct.
Mortality gain (actual lighter than basis — favorable):
Interest gain (actual below basis — unfavorable):
Expense gain (actual below basis — favorable):
Mortality gain (actual lighter than basis — favorable):
Interest gain (actual below basis — unfavorable):
Expense gain (actual below basis — favorable):
Question 3
Hard
A 3-year profit signature: , , , . Test both the IRR criterion (target ) and DPP criterion (target years) at .
Solution
D is correct.
Compute NPV at :
Since , IRR , so the IRR criterion fails.
DPP at :
Year 1:
Year 2:
Year 3:
The cumulative NPV never reaches zero within 3 years, so the DPP exceeds 3 years, also failing the target.
Compute NPV at :
Since , IRR , so the IRR criterion fails.
DPP at :
Year 1:
Year 2:
Year 3:
The cumulative NPV never reaches zero within 3 years, so the DPP exceeds 3 years, also failing the target.
