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FRM Part I · FRM Exam Part I · Insurance Companies and Pension Plans

A defined benefit plan's liabilities are valued by discounting promised benefits at a high-quality corporate bond rate. Interest rates fall by 100 basis points while plan assets are mostly equities that are unchanged in value. Liability duration is 12 years. Approximately what is the effect on the plan's funded ratio, starting from fully funded (assets = liabilities = USD 200 million)?

Falling rates raise the present value of liabilities by roughly 12%, from USD 200 million to about USD 224 million, while equity assets stay at USD 200 million. The funded ratio therefore drops to about 89%, showing the plan's interest rate mismatch.

  1. AFunded ratio rises to about 112%
  2. BFunded ratio falls to about 89%Correct
  3. CFunded ratio is unchanged
  4. DFunded ratio falls to about 98%

Explanation

Liabilities rise by about duration x yield change = 12 x 1% = 12%, to 224 million. Assets remain 200 million. Funded ratio = 200/224 = 89.3%. A rise would require rates to increase, and unchanged ignores the discount rate sensitivity.

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