Shiller (2003) and others have argued for the creation of financial instruments that allow households to insure risks associated with their lifetime labor income. In this paper, we argue that while the purpose of such assets is to smooth consumption across states of nature, one must also consider the assets' effects on households' ability to smooth consumption over time. We show that consumers in a realistically calibrated life-cycle model would generally prefer income-linked loans (with a rate positively correlated with income shocks) to an income-hedging instrument (a limited liability asset whose returns correlate negatively with income shocks) even though the assets offer identical opportunities to smooth consumption across states. While for some parameterizations of our model the welfare gains from the presence of income-linked assets can be substantial (above 1 percent of certainty-equivalent consumption), the assets we consider can only mitigate a relatively small part of the welfare costs of labor income risk over the life cycle.