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

A pension plan's liabilities are discounted at the rate of high-quality corporate bonds. If that discount rate falls by 50 basis points and the liabilities have a duration of 14 years, approximately how does the present value of liabilities change, ignoring convexity?

Liabilities rise by about 7.0%. With a duration of 14 years, a 0.50% fall in the discount rate raises present value by roughly 14 times 0.005, or 7%. Lower discount rates increase the value of future obligations, worsening the funding position unless assets rise similarly.

  1. AIncrease of about 7.0%Correct
  2. BDecrease of about 7.0%
  3. CIncrease of about 0.7%
  4. DDecrease of about 0.7%

Explanation

Percentage change ≈ -Duration × Δy = -14 × (-0.005) = +7.0%. A fall in the discount rate raises the present value of liabilities. The decrease options have the wrong sign, and 0.7% comes from treating 50 bp as 0.05%.

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