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IBBC CAPITAL ACADEMY / 2027

Match a pension liability without confusing price risk

Independent IBBC Capital draft content for self-study. Not affiliated with or endorsed by CFA Institute. New lessons await subject-matter review. No CFA designation or official PSM credit is awarded.

Learning goals

  • Calculate liability and asset dollar durations.
  • Determine the hedge direction and number of contracts under the stated units.
  • Explain two risks remaining after the first-order hedge.

Draft · approximately 35 minutes, excluding further revision.

Case facts

A fictional pension plan has liability PV of 100 million and modified duration 8. Assets total 110 million with modified duration 6. Both use the same currency and a small parallel-yield-shift model. A proposed interest-rate futures contract has dollar duration 800,000 per unit of decimal yield per contract, defined as the change in currency value for a 1.00 change in yield. Futures basis risk, convexity and cash-flow timing are not modeled in that number.

The committee wants to reduce first-order surplus sensitivity while preserving a liquidity reserve. No contract is assumed to remove all pension risks.

Decision framework

For a small parallel shift Δy, ΔPV≈−PV×Dmod×Δy. Matching durations alone is insufficient when asset and liability PVs differ; match dollar duration, then assess convexity, key-rate exposures, basis and liquidity separately. A long bond futures position adds positive rate duration under the simplified contract convention.

Formula and assumptions

Decision → calculation/evidence → case-specific reason → limitation

Compare with the model response after drafting
  1. Liability dollar duration=100m×8=800m; asset dollar duration=110m×6=660m, both per unit decimal yield.
  2. The gap is 140m. Add duration by going long 140,000,000/800,000=175 contracts. The input is equivalent to 80 of currency value per basis point per contract; a real contract specification must be verified.
  3. Nonparallel curve shifts and convexity mismatch can leave residual surplus risk. Futures variation margin can create liquidity needs despite an economic hedge; liability estimates may change independently.

Errors to catch

  • State a recommendation only after identifying the case constraint and calculation.
  • Rubric results are your self-assessment, not an official or AI grade.

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Sources and coverage status

These original lessons are drafts. Public outlines are used to check scope; the official learning-outcome text and proprietary question banks are not reproduced here. Follow the source for exam-year requirements and updates.