People dislike inflation because inflation erodes the real value of future nominal income and wealth. Adjustment of future nominal values via a cost of living index is an appropriate way to handle the problem of real income risk. Nonetheless an important aspect needs more discussion: If markets existed in which real income risks could be traded-would a rational individual always voluntarily purchase protection against such risk? A model is developed to shed some light on this aspect. It shows that the optimal behaviour depends - as expected - on the cost of protection and the risk preferences of the individual.