This paper shows that, in the absence of a complete set of risk markets, prices provide incorrect signals for guiding production decisions. Even if all individuals have rational expectations concerning the distribution of prices which will prevail on the market next period, the market allocation is, in general, not a constrained Pareto optimum. Essentially the only conditions under which, for all technologies, the market equilibrium is a constrained Pareto optimum are those in which risk markets are redundant. We derive the necessary and sufficient conditions for redundancy of risk markets, which turn out to be extremely restrictive.