# Variance(endowment) < [variance(pure endowment)+variance(term assurance)

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I have proven thatÂ Variance(endowment) < [variance(pure endowment)+variance(term assurance)] mathematicallyrics. I would like to know why this is true intuitively : question 1.19

answered Jun 26, 2017 by (2,950 points)

One way to look at this is to consider the sources of 'uncertainty' that each product essentially exhibits.

For the pure endowment, there is uncertainty as to whether a payment will have to be made at the end of the period.

For the term assurance, the uncertainty is the timing of the payment (provided the life dies before the end of the term); and whether a payment will actually occur.

Whereas for the endowment, the only uncertainty is the timing of the benefit, not whether a benefit will be paid.

Uncertainty(endowment) = timing

Uncertainty(pure endowment) = amount

Uncertainty (term assurance) = amount and timing

So if you add the 'uncertainty' components, you will get the uncertainty of the endowment should be lower than the uncertainty of the pure endowment and term assurance, i.e.