FAM: Aggregate loss variance needs both frequency and severity

For independent identically distributed severities independent of frequency, E[S]=E[N]E[X] and Var(S)=E[N]Var(X)+Var(N)E[X]². The second term reflects how many losses occur. Independence assumptions are part of the answer.

Worked example or practice scenario

Let N be Poisson with mean 3, severity mean 100 and variance 4,000. Expected aggregate loss is 300. Variance is 3×4,000 + 3×100² = 42,000. Using only 12,000 treats the loss count as fixed.

Try this next

Replace N with a fixed count of 3 and compare the variance. Next ask what changes if a common weather factor affects both claim frequency and severity; the simple independence formula no longer automatically applies.

Reading sources

• Official syllabus and resources

ActNet editorial guide · October 1, 2026 · Original illustrative examples.