This article studies how health and wealth investments react to the presence of random returns, distinguishing the case where only the level of health investment is chosen from the case where both health and wealth investments are chosen. We show that this reaction depends mainly on certain features of preferences: cross‐prudence/imprudence in wealth, cross‐prudence/imprudence in health, and the value of the indexes of relative prudence in wealth and in health being larger or smaller than the threshold of 2. We also show the role of Edgeworth–Pareto substitutability/complementarity between wealth and health investments in determining optimal choices.