Sample Questions
Question 1
Easy
Duration matching in immunization is most analogous to:
Solution
C is correct.
Duration matching is analogous to a balanced seesaw. The liability is at one point (the fulcrum/horizon), and the portfolio's weighted average cash flow timing must balance at the same point. If interest rates change, the asset and liability values change by the same amount (like both sides of a seesaw moving equally), maintaining equilibrium.
Duration matching is analogous to a balanced seesaw. The liability is at one point (the fulcrum/horizon), and the portfolio's weighted average cash flow timing must balance at the same point. If interest rates change, the asset and liability values change by the same amount (like both sides of a seesaw moving equally), maintaining equilibrium.
Question 2
Medium
Measurement risk in immunization refers to the risk that:
Solution
C is correct.
Measurement risk arises when the statistical inputs used for immunization (duration, convexity, present value calculations) are inaccurately estimated. Sources of measurement error include using approximate duration formulas, ignoring optionality in callable bonds, using incorrect yield curve models, or misestimating cash flow timing. These errors can cause the actual immunization to deviate from the intended match.
Measurement risk arises when the statistical inputs used for immunization (duration, convexity, present value calculations) are inaccurately estimated. Sources of measurement error include using approximate duration formulas, ignoring optionality in callable bonds, using incorrect yield curve models, or misestimating cash flow timing. These errors can cause the actual immunization to deviate from the intended match.
Question 3
Hard
Suppose Vasquez acts on the view in Exhibit 3 and sizes the futures overlay to achieve only a 50% hedge ratio (rather than the 75% target). If 10-year yields then rise 25 bps across the liability curve as she expects, the change in the plan's surplus (assets − liabilities) is closest to:
Solution
A is correct.
Surplus hedging with futures: effective asset BPV = hedge ratio × liability BPV; ΔSurplus = −(asset BPV × Δy) − (−liability BPV × Δy).
| Step | Calculation | Result |
|---|---|---|
| Effective asset BPV | 0.50 x $3,600,000 | $1,800,000 |
| Asset side change | $1,800,000 x 25 bp | ($45.0 million) |
| Liability side change | $3,600,000 x 25 bp | ($90.0 million) |
| Surplus change | −$45.0 million − (−$90.0 million) | +$45.0 million |
| **Change in surplus** | **+$45.0 million** | |
Under-hedging (50% vs the 75% target) leaves the plan with positive net duration exposure to falling liability values, so the surplus gains when yields rise as Vasquez expects.
Surplus hedging with futures: effective asset BPV = hedge ratio × liability BPV; ΔSurplus = −(asset BPV × Δy) − (−liability BPV × Δy).
| Step | Calculation | Result |
|---|---|---|
| Effective asset BPV | 0.50 x $3,600,000 | $1,800,000 |
| Asset side change | $1,800,000 x 25 bp | ($45.0 million) |
| Liability side change | $3,600,000 x 25 bp | ($90.0 million) |
| Surplus change | −$45.0 million − (−$90.0 million) | +$45.0 million |
| **Change in surplus** | **+$45.0 million** | |
Under-hedging (50% vs the 75% target) leaves the plan with positive net duration exposure to falling liability values, so the surplus gains when yields rise as Vasquez expects.
