In the expected-utility theory of the monetary value of a statistical life, a well-known result found by Pratt and Zeckhauser  asserts that an individuals’ willingness to pay (WTP) for a marginal reduction in mortality risk increases with the initial level of risk. Their reasoning is based on the so-called “dead-anyway effect” which states that marginal utility of a dollar in the state of death is smaller than in the state of survival. However, this explanation is based on the absence of markets for contingent claims, i.e. annuities and life insurance. This paper reexamines the relationship between WTP and the level of risk under more general circumstances and establishes two main results: first, when insurance markets are perfect, for a risk-averse individual without a bequest motive, marginal WTP for survival does increase with the level of risk but this occurs for a different reason, namely an income effect. Secondly, when the individual has a bequest motive and is endowed with a sufficient amount of wealth from human capital, the effect of initial risk on WTP for survival is reversed: the higher initial risk the lower the value of a statistical life. In the imperfect-markets case we interpret this result as a “constrained-bequest effect”.