The preferences of a decision-maker who faces risk on two different dimensions
depend both on the curvature of her indifference map under certainty, which is a distinctly
ordinal property, and on the degree of concavity of the utility function representing preferences
under risk, which is a cardinal property. The weight of these two components is
shown to depend on the direction of the change in risk. Bidimensional stochastic orders
accounting for risks on any possible direction are rst dened by generalizing the concept
of submodularity. Three different factors are shown to shape individual preferences under
risk in the bidimensional case: the degree of substitutability among goods, the intensity
of risk aversion on each single dimension and the degree of correlation aversion of the
decision-maker. Their contributions to the amount of risk premium is assessed and a new
notion of "compensated risk aversion" is introduced.