The equivalence between multiportfolio time consistency of a dynamic
multivariate risk measure and a supermartingale property is proven.
Furthermore, the dual variables under which this set-valued supermartingale is
a martingale are characterized as the worst-case dual variables in the dual
representation of the risk measure. Examples of multivariate risk measures
satisfying the supermartingale property are given. Crucial for obtaining the
results are dual representations of scalarizations of set-valued dynamic risk
measures, which are of independent interest in the fast growing literature on
multivariate risks.