This paper studies the effect of limited commitment on sorting when two sides of a frictionless matching market form pairs to share risk. First, we provide analytical results when risk-sharing contracts condition on current shocks only. We show that (i) if the couple faces no aggregate risk, any stable matching is positive assortative in risk aversion, while (ii) if the correlation of income shocks is non-negative, matching is negative assortative. Second, we propose a numerical algorithm to detect assortativity when transfers are history dependent. Positive assortative matching can be stable both for positive and negative correlation of shocks.