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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Graduation and graduation tests

An actuary has crude mortality rates for ages 40 to 70 from a portfolio of Indian life policies. Which statement best describes the main reason for graduating these crude rates?

Graduation replaces crude rates with smoother estimates that use information from neighbouring ages, because underlying mortality is expected to change smoothly with age while crude rates carry random sampling fluctuations.

  1. ATo remove the effect of the exposed-to-risk definition so that deaths equal expected deaths exactly at every age
  2. BTo replace the crude rates with rates that are smoother and borrow strength from neighbouring ages, because true mortality is expected to vary smoothly with ageCorrect
  3. CTo make the graduated rates reproduce the random fluctuations seen in the observed data
  4. DTo ensure that the total graduated deaths are always lower than total observed deaths
  5. To convert central rates of mortality into initial rates of mortality

Explanation

Crude rates at each age are subject to sampling error, but true mortality is expected to progress smoothly with age. Graduation uses information from adjacent ages to produce smooth estimates. It does not aim to reproduce random noise or force a fixed direction of total deaths.

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