In this article, the diversification motives of the demand for annuities is analyzed. Using a model allowing for the uncertainty of both the human life length and the interest rate, the Decision Maker is supposed to choose an optimal portfolio to maximize a bequest. Conditions under which an increase in the risk of bond returns increase the demand for annuities are proposed and discussed. Moreover, it is shown that, contrary to previous claims, more risk adversion is associated with a lower demand for annuities.