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
For the de-risking step, the candidate portfolio in Exhibit 2 that Vega should recommend is:
Solution
B is correct. Immunizing a stream of liabilities with coupon-paying bonds requires three conditions. First, the initial market value of the assets must be at least the present value of the obligation: each candidate is $612.2 million against $600.0 million. Second, the money duration of the assets must match that of the liability, which is what the shared BPV of $750,000 confirms; the assets carry a slightly lower effective duration, 12.25 against 12.50, precisely because they are the larger pool:
Third, the convexity and cash flow dispersion of the assets must be at least as large as the liability's, so that a twist in the curve does not leave the assets behind, yet no larger than necessary, since dispersion is what exposes an immunized position to a change in curve shape.
Candidate A's convexity of 196 is below the liability's 214 and its dispersion of 21.4 is below 28.5; its payments are more tightly clustered than the benefits they fund, so a non-parallel move can push asset value below the obligation. Candidate C satisfies the inequality but with convexity of 305 against 214 and dispersion of 62.8 against 28.5, a barbelled layout whose surplus swings materially when the curve flattens or steepens. Candidate B carries the smallest excess over the liability on both measures, 228 against 214 and 33.7 against 28.5, and therefore minimizes structural risk while preserving the convexity cushion Vega needs ahead of the buyout.
Third, the convexity and cash flow dispersion of the assets must be at least as large as the liability's, so that a twist in the curve does not leave the assets behind, yet no larger than necessary, since dispersion is what exposes an immunized position to a change in curve shape.
Candidate A's convexity of 196 is below the liability's 214 and its dispersion of 21.4 is below 28.5; its payments are more tightly clustered than the benefits they fund, so a non-parallel move can push asset value below the obligation. Candidate C satisfies the inequality but with convexity of 305 against 214 and dispersion of 62.8 against 28.5, a barbelled layout whose surplus swings materially when the curve flattens or steepens. Candidate B carries the smallest excess over the liability on both measures, 228 against 214 and 33.7 against 28.5, and therefore minimizes structural risk while preserving the convexity cushion Vega needs ahead of the buyout.
