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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Death strain at risk, expected and actual death strain, mortality profit

A portfolio has 2,000 identical policies in force at the start of the year. Each has sum assured Rs 5,00,000 payable at the end of the year of death, and the end-of-year reserve for a survivor is Rs 40,000 per policy. The expected mortality rate is 0.004. During the year 11 policyholders die. What is the actual death strain minus the expected death strain for the portfolio?

Actual death strain exceeds expected by Rs 13,80,000, an adverse result. The death strain at risk is Rs 4,60,000 per policy; expected deaths are 8 giving Rs 36,80,000, while 11 actual deaths give Rs 50,60,000, so the mortality experience produces a loss.

  1. ARs 13,80,000 favourable
  2. BRs 13,80,000 adverseCorrect
  3. CRs 27,60,000 adverse
  4. DRs 13,80,000 adverse, but only if reserves are ignored
  5. Rs 18,40,000 adverse

Explanation

Death strain at risk per policy = 5,00,000 - 40,000 = 4,60,000. Expected deaths = 2,000 x 0.004 = 8, so expected strain = 36,80,000. Actual strain = 11 x 4,60,000 = 50,60,000. Difference = 13,80,000, more than expected, so adverse (mortality loss).

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